Exponential Probabilities Mean Lambda 8000 0.000125 x F(x) 0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 11000 12000 13000 14000 15000 16000 17000 18000 19000 20000 21000 22000 23000 24000 25000 26000 27000 28000 29000 30000 31000 32000 33000 34000 35000 36000 37000 38000 39000 40000 0 0.1175031 0.2211992 0.3127107 0.3934693 0.4647386 0.5276334 0.583138 0.6321206 0.6753475 0.7134952 0.7471604 0.7768698 0.8030883 0.8262261 0.846645 0.8646647 0.880567 0.8946008 0.9069855 0.917915 0.9275602 0.9360721 0.9435839 0.9502129 0.9560631 0.9612258 0.9657819 0.9698026 0.9733509 0.9764823 0.9792457 0.9816844 0.9838365 0.9857358 0.9874119 0.988891 0.9901963 0.9913483 0.9923649 0.9932621 Cumulative Distribution Function 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 nction Profitability Index Analysis Experiment 1 Mean Standard Deviation 2 PV 12 2.5 3 I 3 0.8 4 5 Mean PI for 1000 Experiments 4.432663 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 PV 9.005948 8.912891 12.86575 13.20605 11.89142 14.10561 12.89253 11.91677 11.7953 12.99773 12.73457 9.684299 11.40635 13.86272 16.82002 11.51546 14.14652 13.52687 11.00444 13.95052 12.13427 11.66201 10.89525 16.37781 15.10541 12.81195 12.26105 9.330641 14.1862 13.99475 10.88506 11.49726 15.55527 9.425506 9.093846 11.10973 15.41152 8.505987 14.78089 14.00053 14.24011 8.420545 9.072619 9.356263 11.15398 18.04362 9.423577 11.26821 13.08626 12.53249 7.404933 15.39483 12.90603 15.44476 11.70032 9.207284 I 3.027045 2.239562 3.073938 3.093797 3.590273 3.744341 2.611085 3.441819 3.449641 3.389656 2.515951 4.20902 2.556244 3.56856 3.67395 3.177164 2.943133 3.670958 3.666406 2.175388 2.486744 2.275311 2.561531 4.401521 3.636152 3.121923 2.606412 3.255063 2.427299 2.785056 2.602778 3.735054 3.968492 3.326345 2.355984 3.04345 4.278854 3.282264 2.353764 2.340876 2.991205 2.684308 1.945564 2.742697 2.532635 3.015659 2.370166 1.808304 0.466106 3.566467 3.464312 3.918901 4.012883 3.232517 2.855701 3.478711 PI 2.975162 3.979748 4.185429 4.268559 3.312121 3.767182 4.937613 3.462345 3.419283 3.834529 5.061535 2.300844 4.462151 3.884682 4.578185 3.624447 4.806619 3.684835 3.001424 6.412888 4.87958 5.125459 4.253411 3.720943 4.15423 4.103865 4.704188 2.866501 5.844439 5.024944 4.182091 3.078204 3.919692 2.833593 3.859893 3.650374 3.601787 2.5915 6.279683 5.980893 4.76066 3.136952 4.663233 3.411337 4.404101 5.983308 3.975914 6.23137 28.07569 3.513979 2.13749 3.928355 3.216149 4.777936 4.097179 2.646751 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 12.43498 16.16235 11.0048 12.08928 6.723989 11.74003 7.628203 8.343261 15.43015 10.56446 15.55402 12.74929 12.93447 13.0796 12.55983 15.55769 10.03799 7.256543 11.83662 12.2021 12.98109 11.967 10.88868 9.611644 16.19166 9.504774 8.114889 13.00503 14.84004 10.25799 5.633273 8.792246 13.22275 10.87816 12.39039 13.1026 12.52483 17.17589 7.016049 11.27097 12.10477 12.10811 12.45858 11.51067 13.5721 13.52589 11.07104 19.81244 11.65851 15.6303 10.8836 13.97918 11.38124 12.54855 13.33864 14.07605 7.987271 2.834374 3.117143 1.958039 3.203592 1.61031 1.216056 1.727963 2.689342 1.777473 3.463381 3.935198 0.564666 2.828704 2.38586 2.593368 4.412762 3.51337 2.964691 2.649991 0.813565 2.561412 0.620644 3.457293 2.791782 2.479511 2.480968 3.743665 2.775608 2.609028 3.671901 2.986069 3.155343 2.837957 3.07184 2.219378 3.455413 2.053234 3.153417 3.194321 2.425277 2.305438 3.726326 3.142702 3.305049 2.183928 3.858866 1.892257 2.740486 3.535963 1.987384 3.582613 3.050412 2.712973 3.073089 2.942284 2.662656 3.169624 4.387204 5.184988 5.620313 3.773664 4.175587 9.654187 4.414563 3.102342 8.680946 3.050332 3.952538 22.57847 4.572576 5.482134 4.843055 3.525613 2.857083 2.447655 4.466663 14.99831 5.067944 19.28158 3.149481 3.442835 6.53018 3.831075 2.167632 4.685472 5.687959 2.793644 1.886518 2.786463 4.659248 3.541252 5.582821 3.791907 6.100052 5.446753 2.196413 4.64729 5.250531 3.249342 3.964288 3.482753 6.214533 3.505146 5.850707 7.229536 3.297124 7.864759 3.037896 4.58272 4.195116 4.083367 4.533431 5.286471 2.519943 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 11.41518 11.58653 7.273958 9.249157 14.57603 10.34025 11.43253 19.26502 13.12764 12.30704 12.1852 11.73727 15.97012 9.545487 9.376823 8.597946 13.19906 10.94528 12.37961 12.42751 11.76946 10.53468 10.7212 13.50995 11.65784 8.916001 12.61317 12.55204 12.63938 16.00119 10.32642 11.80154 2.961801 8.5688 13.43045 10.70641 9.890975 10.54998 11.28674 10.53119 12.46353 13.87669 14.44481 10.82971 13.47783 12.58732 17.58478 14.42593 13.34071 11.72616 14.18054 8.654147 13.76773 6.233681 13.44811 14.01753 4.987054 2.657246 3.355359 2.322244 2.506537 3.326511 2.64362 2.587951 5.828676 2.2596 2.805166 3.482932 3.610553 2.035588 0.879083 3.836163 1.786302 3.023615 2.645407 1.990962 4.510339 2.85023 3.941465 4.001124 3.787887 2.296299 2.865844 3.364907 3.068603 2.985807 2.494735 2.416596 3.68205 2.680808 3.489814 1.90522 1.577949 2.487222 3.681021 2.998437 3.128842 3.577019 3.484027 3.875638 3.812039 2.619731 3.342033 1.561068 3.569849 2.825648 2.159676 2.96084 2.375011 1.85073 2.270503 4.708437 4.339037 1.79565 4.295869 3.453143 3.132298 3.690015 4.381778 3.911399 4.417601 3.305214 5.809718 4.387279 3.498548 3.250824 7.845456 10.85846 2.444323 4.813265 4.365325 4.137464 6.217902 2.755338 4.129302 2.672782 2.679546 3.566618 5.076794 3.111126 3.748445 4.090473 4.233153 6.413983 4.273129 3.205155 1.104816 2.455375 7.04929 6.785016 3.976715 2.866048 3.764209 3.365842 3.484335 3.982945 3.72708 2.840922 5.144737 3.766367 11.26459 4.041049 4.721292 5.429591 4.789363 3.643834 7.439081 2.745507 2.856173 3.230563 2.777298 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 15.4105 18.00075 8.753371 9.369581 10.29409 12.30829 9.655186 9.198661 9.073228 14.37626 13.52892 8.634043 9.759952 12.62111 11.87985 14.37418 8.301587 14.13004 9.901953 13.09795 10.94959 10.99003 13.38253 7.394601 12.56237 11.42022 9.941418 9.740452 8.209263 11.3676 11.7423 10.94251 14.67586 14.33214 10.11821 8.607982 9.065605 14.65972 11.03263 13.84709 13.9923 12.28032 13.54818 8.124892 10.92018 11.90574 13.71793 11.61483 9.669717 9.637931 10.75414 12.0537 8.388951 11.7792 10.53955 15.04193 10.52119 3.731463 3.72678 3.042268 3.212227 2.776896 2.839586 3.051465 3.132011 1.515269 4.12259 3.508281 3.243909 2.88958 3.463508 2.068462 4.050494 3.738517 2.720335 3.059567 3.063122 3.465232 2.480112 3.79018 2.729305 2.393003 2.640981 3.080164 3.231681 2.560925 3.328106 2.017301 2.664219 3.692531 4.490773 3.163475 3.994626 4.604756 4.25428 2.149273 4.617751 3.479349 1.806883 4.624021 2.627029 4.362144 2.916428 3.475012 2.786802 3.124678 1.113161 3.372886 1.588708 4.372763 2.248517 3.376806 2.84738 2.363474 4.12988 4.830108 2.877252 2.916849 3.707051 4.334536 3.164115 2.936983 5.987868 3.487191 3.85628 2.661617 3.377637 3.644025 5.743323 3.548746 2.220556 5.194228 3.23639 4.276013 3.159845 4.431261 3.530844 2.709335 5.249624 4.324234 3.227561 3.014052 3.205586 3.415638 5.820797 4.107213 3.974473 3.191465 3.198448 2.154891 1.968748 3.445877 5.133194 2.998664 4.021527 6.796411 2.929956 3.092806 2.503397 4.082301 3.947593 4.167799 3.094628 8.658166 3.188408 7.587105 1.918455 5.238656 3.12116 5.282726 4.451577 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 11.82221 13.65413 13.84819 16.18111 14.83837 12.49026 7.841221 9.404312 12.18171 10.40185 8.306004 12.89869 9.543342 9.422816 12.92032 14.18224 13.37861 13.48011 12.86361 11.03003 10.93698 14.21411 15.01568 8.278526 12.60725 9.834785 14.53021 13.88228 10.68737 11.28452 13.45943 9.842392 11.67724 8.858577 14.52978 13.07263 10.61918 12.07153 13.45556 15.49187 15.9383 15.32928 12.73348 13.99152 7.982502 11.60744 13.58549 11.80369 10.17529 10.59996 15.39819 11.23663 10.3987 11.77574 10.80364 7.810888 12.78743 3.015079 3.161603 2.932991 3.8342 3.244269 3.161712 2.156728 1.964299 3.558995 2.739545 2.553129 1.834033 2.773728 2.35422 3.192297 3.206019 4.433428 2.789413 3.216936 2.612992 2.125352 2.213155 3.646511 2.33099 3.312923 2.512415 2.404468 2.936181 3.417626 2.986613 3.752759 1.944091 2.837488 3.096677 3.207636 3.554824 3.459511 2.719568 3.224759 4.575555 3.203496 2.802929 1.994624 3.68073 0.413899 2.48905 4.103936 2.812492 3.057225 3.349976 4.579382 1.800658 2.083722 3.716292 3.829208 3.731732 3.095063 3.921029 4.318735 4.721523 4.220205 4.573716 3.950473 3.635702 4.787616 3.422796 3.796927 3.253264 7.032967 3.440619 4.002521 4.047343 4.42363 3.017666 4.832597 3.998714 4.221225 5.145964 6.422556 4.117821 3.551507 3.805477 3.914475 6.043003 4.728006 3.127132 3.778366 3.586544 5.062722 4.115343 2.860672 4.529747 3.677433 3.069559 4.438766 4.172579 3.38579 4.975284 5.469023 6.383901 3.801288 19.28609 4.663401 3.310357 4.196878 3.328277 3.164188 3.362505 6.240289 4.990442 3.16868 2.821378 2.0931 4.131558 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 11.3489 10.67303 17.20556 11.08226 10.12599 11.58913 14.65343 13.24733 12.13178 11.35816 9.886764 13.99287 10.28412 13.61355 13.96716 14.74278 9.121121 11.7415 11.32733 14.9513 13.82856 9.97825 12.56349 17.61254 13.35762 13.1996 12.56997 9.234787 14.2623 15.02825 13.11374 13.7253 11.48197 14.0268 11.31988 11.46317 12.10064 7.45758 11.36604 12.54554 13.88377 9.483384 17.42119 10.39251 11.57439 9.670129 10.86428 13.03808 12.15427 13.02758 7.319703 12.44222 14.27322 14.82388 12.8222 13.52776 13.51181 3.457573 3.641869 1.057887 3.952875 3.288335 2.778181 2.65982 2.167462 4.117611 3.486155 1.557854 3.55589 3.052844 2.369526 1.212993 1.781644 3.401447 2.150281 1.823076 4.397237 3.599527 3.187188 4.664947 2.745117 2.383039 2.599752 2.144542 2.712642 2.784873 2.392201 3.05745 4.303433 2.495842 0.857074 3.728745 2.957797 4.256652 2.811864 3.368052 6.197539 2.931189 2.560909 3.813078 2.492588 1.045366 2.956413 3.172097 2.939758 2.636063 2.654288 4.198175 1.988324 2.03485 3.939058 2.403504 4.063404 2.903453 3.282332 2.930647 16.26407 2.803595 3.079366 4.171481 5.509183 6.111908 2.946316 3.258077 6.346399 3.935124 3.368702 5.745263 11.51462 8.274815 2.681541 5.460449 6.213307 3.400158 3.841771 3.130738 2.693168 6.415954 5.605288 5.077255 5.861376 3.404352 5.121348 6.282184 4.289112 3.189383 4.60044 16.36592 3.035843 3.875576 2.84276 2.652183 3.374663 2.024278 4.736564 3.703132 4.5688 4.169365 11.0721 3.270899 3.424952 4.435085 4.610765 4.908126 1.743544 6.257642 7.014382 3.763305 5.334792 3.329169 4.653704 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 13.73693 11.56166 15.97178 9.598879 10.88315 14.45927 13.09718 13.74458 12.14452 8.893468 10.27811 12.15563 10.67567 8.993411 8.217597 16.13482 12.7521 13.12523 11.67647 9.826406 17.62628 12.24286 12.36385 10.99018 11.51472 9.82505 8.220783 12.09493 11.4306 11.97421 9.605152 11.87936 17.1335 17.36639 12.43067 15.96289 10.58236 6.113868 15.17398 11.05466 11.51934 10.89227 11.9193 13.00072 9.297288 7.914905 15.31068 12.20683 11.4689 14.55249 7.740072 8.98101 10.29469 12.51883 13.71148 10.40773 12.78914 3.220013 3.915779 2.192083 2.435216 3.568111 2.88744 1.915472 2.699275 2.420323 4.103877 2.936087 3.937579 2.540875 1.609384 2.711091 3.247997 3.181275 2.345641 2.71439 3.609314 2.348318 2.571723 1.642233 4.393345 4.212362 2.620998 3.360814 2.239935 2.614704 1.46374 2.573878 2.809016 2.397009 3.387904 2.424202 2.846453 2.610428 2.916848 2.758573 2.930019 3.967741 4.020144 4.063521 2.332261 3.069015 2.340586 1.350536 3.502216 3.054248 3.429723 2.67916 3.374243 3.711014 3.160529 3.906921 2.493252 4.051236 4.266111 2.952583 7.286121 3.941695 3.050115 5.007643 6.837575 5.091951 5.017725 2.167089 3.500614 3.087082 4.20157 5.588107 3.031103 4.967621 4.008488 5.595585 4.301692 2.722514 7.505917 4.760567 7.528682 2.501552 2.733555 3.748591 2.446069 5.39968 4.37166 8.180561 3.731783 4.229012 7.147865 5.125999 5.127739 5.607996 4.053877 2.096053 5.500665 3.772897 2.903249 2.709422 2.933244 5.574297 3.029405 3.38159 11.33674 3.485459 3.755064 4.243051 2.888992 2.661637 2.77409 3.960993 3.509536 4.174359 3.156849 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 450 451 452 453 454 455 10.42252 12.07962 15.14598 10.0219 16.6567 9.918873 12.77712 14.39172 13.14251 10.54114 9.478611 13.64618 11.97984 13.77606 8.788277 12.34272 12.13773 7.669683 11.44204 16.01971 11.78213 11.64142 15.96316 12.93668 11.34348 12.12154 13.69901 11.67949 15.07936 8.498704 16.74968 10.90305 13.44243 7.973544 10.41666 14.14773 15.73184 12.67304 10.52303 10.29653 14.55117 14.52007 10.56681 5.093754 10.50026 13.00465 15.4929 12.56215 9.736404 11.03565 10.25778 13.79156 7.935552 10.26118 12.33469 14.75524 12.93005 2.263044 2.905557 3.635817 3.930812 2.565649 2.06871 3.545046 2.378427 2.707543 2.984742 4.653222 2.733379 3.626678 2.847431 2.932328 2.860023 2.266181 3.426737 2.838002 2.600562 4.215101 3.206867 2.148515 3.141882 1.338474 3.338458 1.824266 4.178652 3.573251 3.894842 2.865513 2.485991 2.709065 2.885911 3.710224 3.983267 3.35781 3.563435 2.1881 3.637788 2.40401 1.5728 2.671148 2.866792 2.821823 3.325178 2.601679 2.929698 2.639435 1.801335 3.629262 3.632424 2.56392 4.151477 2.192022 2.124788 4.416089 4.605534 4.157421 4.165771 2.549576 6.492199 4.794713 3.604218 6.050942 4.854037 3.531676 2.036999 4.992423 3.303254 4.838066 2.997031 4.315603 5.356028 2.238189 4.031722 6.160095 2.795218 3.630154 7.429859 4.117493 8.474931 3.630881 7.509328 2.795039 4.220067 2.182041 5.845266 4.385798 4.96202 2.762921 2.807557 3.55179 4.68515 3.556411 4.809207 2.830438 6.052876 9.231991 3.955905 1.776813 3.721091 3.910964 5.954963 4.287866 3.688821 6.126371 2.82641 3.796793 3.095086 2.471693 5.627084 6.944338 2.927942 456 457 458 459 460 461 462 463 464 465 466 467 468 469 470 471 472 473 474 475 476 477 478 479 480 481 482 483 484 485 486 487 488 489 490 491 492 493 494 495 496 497 498 499 500 501 502 503 504 505 506 507 508 509 510 511 512 7.523504 11.32924 13.90421 12.08408 14.87884 11.72679 13.9217 12.0285 9.514928 8.057659 12.11745 14.51984 16.88065 13.13895 8.526459 10.31893 15.16863 10.62483 10.34232 12.06348 12.27692 10.82068 10.95686 13.11246 10.81929 8.548122 8.724252 11.6988 11.93178 13.70917 17.04382 10.66471 12.68366 11.6799 11.5759 14.06018 12.49477 12.77286 13.23088 8.98649 11.24479 12.3913 13.20802 11.48768 13.86844 11.12102 10.25476 11.25682 14.14118 14.96101 12.23833 13.14721 11.5012 13.02773 12.75406 8.73679 12.27971 3.064284 3.274601 3.050668 3.352508 3.088515 3.113113 2.264177 4.091782 2.939507 2.486823 3.132112 1.691233 2.637632 3.666552 2.229812 3.887427 2.455657 2.986537 2.551636 3.684166 2.02775 4.711264 3.157386 2.157447 3.68189 3.835978 3.963531 2.805183 3.097643 2.466657 3.891421 3.031147 2.49959 2.158691 1.974433 1.908824 2.781071 3.52013 3.157989 3.677134 3.438387 2.629295 5.38082 2.659306 2.987834 4.758105 4.662453 2.878791 3.35961 2.920426 1.160847 4.160914 2.629528 3.06782 2.473631 2.553745 3.242421 2.455224 3.459731 4.557757 3.604489 4.817473 3.7669 6.148682 2.939674 3.236913 3.240142 3.868779 8.585356 6.399927 3.583461 3.823847 2.654437 6.177016 3.557574 4.053211 3.274413 6.054456 2.296769 3.470232 6.077769 2.938514 2.228408 2.201131 4.170423 3.851888 5.557793 4.379844 3.518376 5.074297 5.410639 5.862895 7.365887 4.492789 3.628518 4.189653 2.443885 3.270369 4.712785 2.454648 4.319801 4.641638 2.337279 2.199435 3.910259 4.209173 5.122887 10.54259 3.159692 4.373865 4.246578 5.156005 3.421168 3.787205 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528 529 530 531 532 533 534 535 536 537 538 539 540 541 542 543 544 545 546 547 548 549 550 551 552 553 554 555 556 557 558 559 560 561 562 563 564 565 566 567 568 569 11.97604 11.94056 13.69245 9.94354 9.598074 9.104617 14.56441 12.90777 12.50364 9.841748 8.946319 12.64002 13.07613 10.15417 8.717911 8.218347 15.78254 13.61418 13.5406 13.64813 13.2277 10.65477 12.33015 13.13829 10.42059 12.38861 10.02736 8.83718 11.73404 11.7465 10.28493 9.885212 12.18337 12.1419 13.18916 11.09755 10.04061 14.49922 9.382202 11.677 12.60308 12.97679 10.00241 8.969992 10.73392 13.93154 16.78329 10.5091 11.33109 12.2129 10.15221 14.65853 9.861717 12.47478 12.41786 14.04706 12.39119 2.44474 2.362277 2.89036 2.807506 3.812765 2.524038 3.228157 3.186907 2.351763 2.183407 2.013501 2.033633 4.139937 3.696666 2.974716 2.531559 2.112772 3.021509 3.951837 2.229363 2.828703 2.611951 3.124922 4.867161 1.940426 3.691953 1.910599 2.072745 2.887936 4.212837 2.401837 2.230886 1.672277 1.673356 2.070374 2.835418 1.942244 1.981356 2.983742 1.733543 2.70769 3.245512 4.534412 2.197966 2.289915 3.27223 4.558156 3.235819 1.662642 1.433018 4.291602 2.150107 3.189844 3.100198 2.561126 3.35865 3.768668 4.898697 5.054683 4.737282 3.54177 2.517353 3.607164 4.511679 4.050249 5.31671 4.507519 4.443166 6.215489 3.158534 2.746847 2.93067 3.246358 7.470066 4.505756 3.426406 6.121985 4.676242 4.079239 3.945746 2.699375 5.370258 3.355571 5.248278 4.263516 4.063123 2.788264 4.282111 4.43107 7.285496 7.256014 6.370427 3.913902 5.169594 7.317824 3.144441 6.735914 4.654551 3.99838 2.205888 4.081042 4.687474 4.257505 3.682035 3.247742 6.815113 8.522498 2.365599 6.817582 3.091598 4.023865 4.848595 4.182354 3.28795 570 571 572 573 574 575 576 577 578 579 580 581 582 583 584 585 586 587 588 589 590 591 592 593 594 595 596 597 598 599 600 601 602 603 604 605 606 607 608 609 610 611 612 613 614 615 616 617 618 619 620 621 622 623 624 625 626 9.674118 11.39543 9.351496 9.860145 11.11174 15.16524 13.50001 11.86129 14.39419 12.66184 11.0821 16.24521 14.83559 10.71296 14.49159 14.52997 12.21771 10.48893 11.32458 10.223 12.05744 12.73304 12.54831 9.39787 10.81121 14.28712 9.999652 8.863374 12.94692 13.89902 14.3878 13.42236 11.1284 13.05364 10.8984 17.45153 14.62603 10.76095 12.72762 13.79477 10.44568 9.303585 12.44237 10.65 11.1187 9.624938 9.816791 8.872557 7.846042 9.2132 12.43059 17.70133 11.25486 12.59415 12.67898 12.00993 14.76456 2.756241 1.968836 2.324448 2.964896 3.834862 2.065056 3.360642 2.772091 3.177488 2.31804 3.632295 3.895406 2.871623 3.963825 3.067287 4.578277 3.584814 3.741083 3.189875 3.030559 2.731394 1.845736 2.893657 3.389226 3.067085 3.456211 3.83254 4.079664 2.045138 3.202153 3.330439 3.214578 3.597335 3.27883 3.011448 2.971349 2.339465 4.47472 2.148808 3.37241 3.930284 4.776315 3.565852 2.406984 1.832757 2.838889 2.36337 2.085097 3.485475 1.905954 3.414315 2.230098 1.926476 3.758494 2.797549 3.455365 3.78939 3.509895 5.787903 4.023105 3.32563 2.897558 7.343744 4.017093 4.278824 4.530054 5.462304 3.05099 4.170351 5.166275 2.702683 4.724563 3.173678 3.408186 2.803714 3.550165 3.373304 4.41439 6.898626 4.336488 2.772866 3.524913 4.133753 2.609145 2.172575 6.330586 4.340523 4.320092 4.175467 3.093511 3.981188 3.618992 5.87327 6.251871 2.404832 5.923109 4.090479 2.657741 1.947858 3.489311 4.424624 6.066653 3.390389 4.153727 4.255225 2.251068 4.833904 3.640725 7.937467 5.842199 3.35085 4.532172 3.475733 3.89629 627 628 629 630 631 632 633 634 635 636 637 638 639 640 641 642 643 644 645 646 647 648 649 650 651 652 653 654 655 656 657 658 659 660 661 662 663 664 665 666 667 668 669 670 671 672 673 674 675 676 677 678 679 680 681 682 683 17.49839 8.955281 11.23353 5.847673 12.80353 15.48764 12.96146 17.58734 15.76312 14.01688 13.86368 12.98023 12.9293 10.97597 14.32326 8.651074 16.15915 15.29143 7.95174 11.79737 16.38868 11.99738 8.247689 10.8692 15.28806 8.164776 12.52297 13.54443 9.412085 12.07693 15.49439 9.605498 10.6615 9.29511 11.21851 7.840624 14.84921 12.10336 17.66215 12.33837 13.27932 15.9588 17.83654 11.81199 16.52545 7.74907 15.50157 12.66835 13.07817 8.470963 9.652979 13.47226 10.25873 11.49855 13.23249 13.45386 13.17528 3.417278 3.936626 4.239216 2.414373 2.763825 3.14539 4.243616 3.990962 2.978198 4.24241 3.221129 2.923458 2.173657 1.956815 1.8506 2.53236 2.899407 2.625856 4.102636 3.734546 3.915523 2.527463 3.467618 3.195981 4.806464 1.719358 1.964222 3.810328 3.17528 1.382016 3.18971 3.709115 3.391613 2.351925 3.236111 4.686407 3.982964 1.769517 4.697192 3.016396 2.879891 1.451105 3.696094 2.065043 3.679814 3.695406 2.754578 0.691938 2.554656 3.536553 3.232813 3.521687 4.30345 2.891213 3.79911 2.527793 4.043728 5.120563 2.274862 2.649908 2.422025 4.632539 4.923917 3.054344 4.406793 5.292839 3.30399 4.303983 4.440025 5.948179 5.609101 7.739791 3.41621 5.573259 5.823408 1.938203 3.158983 4.185565 4.746808 2.378488 3.400895 3.180729 4.748735 6.375534 3.554662 2.964175 8.738636 4.857617 2.589701 3.14349 3.952128 3.466664 1.673057 3.728181 6.839919 3.760151 4.090435 4.611049 10.99769 4.825781 5.719975 4.490839 2.096947 5.627568 18.30849 5.119348 2.39526 2.985938 3.825513 2.383839 3.977065 3.483051 5.322374 3.2582 684 685 686 687 688 689 690 691 692 693 694 695 696 697 698 699 700 701 702 703 704 705 706 707 708 709 710 711 712 713 714 715 716 717 718 719 720 721 722 723 724 725 726 727 728 729 730 731 732 733 734 735 736 737 738 739 740 14.17567 13.00198 12.4492 13.00854 9.587377 11.64531 8.536617 9.523052 14.7052 6.906236 13.93986 12.4919 10.31584 10.26371 16.63332 13.90051 15.34459 10.88925 9.84471 6.165359 19.5012 12.21657 18.43851 7.528767 10.70754 11.90023 7.270195 12.23594 10.84473 12.40497 9.11107 15.5207 13.26914 13.03403 10.97045 13.60502 11.45012 10.45922 12.5428 10.70354 10.63402 11.20554 10.31872 14.84863 9.015511 9.003049 10.75093 13.74526 14.84907 8.91014 13.53439 9.951762 14.29658 10.00268 9.251207 15.57999 13.98246 2.243761 3.793009 3.97398 1.977468 3.668572 2.318996 4.29474 3.470372 2.957692 3.122287 2.75607 2.78875 2.345948 3.087587 3.293136 2.554446 4.232728 3.288374 3.240528 2.093842 2.604184 2.550629 3.649071 2.876092 2.065708 3.173716 2.817233 4.860057 3.929169 1.817726 4.616723 3.293865 2.223136 3.436205 4.591909 3.114154 2.054153 2.50867 4.121693 3.44797 4.540236 1.328222 2.730261 1.669871 1.807596 1.843254 2.959949 4.249525 1.723071 3.236248 2.795088 4.300855 2.311331 2.779758 2.496184 3.203261 3.925758 6.317817 3.427881 3.132678 6.578382 2.613381 5.021703 1.987691 2.744101 4.971849 2.211916 5.057875 4.47939 4.397299 3.324185 5.050905 5.441692 3.625225 3.311439 3.037995 2.94452 7.48841 4.789632 5.052933 2.617707 5.183473 3.74962 2.580616 2.517654 2.760057 6.824447 1.973493 4.712002 5.968658 3.793147 2.389084 4.36877 5.574132 4.16923 3.043118 3.104302 2.342174 8.436495 3.779389 8.892079 4.98757 4.884325 3.632134 3.234541 8.617791 2.753231 4.842205 2.313903 6.185433 3.5984 3.70614 4.863791 3.561722 741 742 743 744 745 746 747 748 749 750 751 752 753 754 755 756 757 758 759 760 761 762 763 764 765 766 767 768 769 770 771 772 773 774 775 776 777 778 779 780 781 782 783 784 785 786 787 788 789 790 791 792 793 794 795 796 797 7.63627 12.87327 12.26873 13.692 10.60045 11.81833 7.423575 15.23576 16.37153 11.80114 14.39508 14.40522 13.10549 13.94436 10.09057 11.09256 12.4274 14.96035 15.28765 10.16017 11.07052 9.56816 15.11006 11.57247 12.60916 10.23727 13.1419 11.7545 14.30723 11.97711 10.5048 11.74148 11.4452 8.743626 12.20187 12.92225 16.38719 12.94053 8.597012 12.19738 12.58216 8.280254 13.57731 8.845886 11.23322 13.13416 12.88563 9.134854 11.84746 13.43379 11.1528 9.769147 7.035123 12.61699 10.82285 11.23133 13.33667 3.310388 2.636377 4.151909 2.862676 4.047073 2.759208 5.407051 2.754282 2.30287 2.038627 1.525308 2.968026 2.76465 2.949278 3.272367 3.713154 2.347113 3.593384 3.396569 2.682859 2.566097 3.410154 2.190083 4.170463 2.181937 1.951703 3.415979 2.388332 3.977607 3.234684 1.820963 3.151213 3.414499 2.652229 3.504307 2.943518 2.908241 2.426148 1.591983 3.856754 3.497109 2.911604 2.882305 3.714537 3.699442 3.473532 2.32037 3.998486 2.974379 4.162648 3.683827 1.57628 3.37377 1.870999 2.372171 5.369411 3.288798 2.30676 4.882941 2.954962 4.782939 2.619287 4.283234 1.372943 5.531663 7.109187 5.78877 9.437491 4.853467 4.740379 4.728058 3.08357 2.98737 5.29476 4.163305 4.50091 3.787067 4.314146 2.805786 6.899307 2.774864 5.778883 5.245302 3.847184 4.921634 3.596944 3.702715 5.768816 3.726019 3.351941 3.296709 3.481964 4.390069 5.634744 5.333777 5.400192 3.162603 3.597874 2.843881 4.710573 2.381423 3.036464 3.781211 5.553264 2.284578 3.983169 3.227223 3.027505 6.197598 2.08524 6.743449 4.562422 2.091724 4.055181 798 799 800 801 802 803 804 805 806 807 808 809 810 811 812 813 814 815 816 817 818 819 820 821 822 823 824 825 826 827 828 829 830 831 832 833 834 835 836 837 838 839 840 841 842 843 844 845 846 847 848 849 850 851 852 853 854 12.33474 13.13181 12.08869 14.10728 15.63988 13.01386 14.66283 14.29969 7.39682 14.58438 10.58103 9.002449 16.75361 13.73679 15.84403 11.70595 15.36321 16.4281 13.85455 9.662334 10.92286 7.273679 12.54749 9.297401 12.38065 7.355375 13.21979 13.67027 8.116449 14.64439 11.0031 10.35301 7.800921 10.91203 13.22785 9.443177 10.04925 10.39277 12.48399 11.56376 19.50773 12.77355 7.174815 13.82682 11.69108 12.21429 18.26059 14.37694 12.69717 14.09963 9.440699 12.64183 10.16486 8.206748 15.53987 9.398164 11.06323 4.036756 2.206025 3.670053 2.933243 3.641498 4.528259 2.224082 3.148534 3.113146 3.471041 2.309503 4.056184 2.671035 3.93654 2.878721 3.643482 3.629562 3.141713 4.516801 1.884355 2.399523 2.788924 2.535309 2.221124 2.428417 2.929364 3.281196 2.48661 3.272446 2.936509 2.535639 3.195651 3.435268 3.375506 1.743767 2.048088 2.50227 2.082102 2.618931 2.276864 4.194543 4.248649 5.4919 2.427252 4.18412 2.246484 2.729469 3.791921 2.444281 3.458959 2.447007 2.782164 2.533645 1.489155 2.24661 2.812495 3.138466 3.055607 5.952703 3.293874 4.809448 4.294904 2.873921 6.592756 4.541699 2.375995 4.201731 4.581519 2.219438 6.272327 3.489559 5.503845 3.212847 4.2328 5.229028 3.067336 5.12766 4.552095 2.608059 4.949098 4.1859 5.098239 2.510912 4.028956 5.497552 2.480239 4.987008 4.339377 3.23972 2.270833 3.23271 7.585793 4.610728 4.016052 4.99148 4.766828 5.078811 4.650739 3.006498 1.306436 5.696491 2.794156 5.437068 6.690161 3.791465 5.194644 4.076266 3.85806 4.543885 4.011949 5.511008 6.917033 3.341575 3.525045 855 856 857 858 859 860 861 862 863 864 865 866 867 868 869 870 871 872 873 874 875 876 877 878 879 880 881 882 883 884 885 886 887 888 889 890 891 892 893 894 895 896 897 898 899 900 901 902 903 904 905 906 907 908 909 910 911 13.72889 10.24247 13.94323 14.58789 9.773724 12.68482 9.279049 12.74932 10.09547 9.22665 9.331237 17.0906 13.37848 11.5874 12.09859 11.08822 10.70258 16.91966 12.93032 12.50504 13.69268 12.96674 15.34169 11.97464 14.92526 10.51306 13.00335 11.22986 10.75461 15.72523 10.90254 14.71786 12.50202 8.894035 10.11572 10.74646 13.2145 13.29124 10.74759 9.648462 11.26387 8.4122 8.488387 11.6434 13.51713 13.59013 8.614295 15.79733 15.07248 17.91294 13.45009 12.42205 15.15875 14.06401 11.81316 11.85588 14.2197 2.149915 4.243143 1.341379 3.835505 2.401381 3.461109 4.340787 2.565111 2.587599 2.111228 2.194126 3.716473 3.42744 2.121992 4.254624 3.024474 3.073655 3.297346 3.37723 2.507869 3.383811 3.127966 2.084357 2.998726 2.944963 2.882195 3.942535 2.23808 2.318743 2.358702 1.476599 2.857719 3.2108 4.310185 4.889294 3.445149 1.932407 3.669812 2.408924 2.537155 2.591199 2.590054 1.83959 2.724938 3.604035 3.179451 3.418596 1.505194 3.45751 3.221438 2.103933 2.36154 2.139963 2.437758 2.708639 2.441335 1.460664 6.385782 2.413888 10.3947 3.803381 4.070044 3.664958 2.137642 4.970281 3.90148 4.370276 4.252826 4.598606 3.903344 5.460625 2.843632 3.666166 3.482038 5.131296 3.828676 4.986321 4.046528 4.145421 7.360398 3.993244 5.068063 3.647589 3.29822 5.01763 4.638122 6.666901 7.38355 5.150213 3.89374 2.063492 2.068952 3.119303 6.838363 3.621776 4.461573 3.802866 4.346972 3.247886 4.614283 4.272904 3.750555 4.274365 2.519834 10.49521 4.359347 5.56054 6.39283 5.260149 7.083652 5.769239 4.36129 4.856308 9.735093 912 913 914 915 916 917 918 919 920 921 922 923 924 925 926 927 928 929 930 931 932 933 934 935 936 937 938 939 940 941 942 943 944 945 946 947 948 949 950 951 952 953 954 955 956 957 958 959 960 961 962 963 964 965 966 967 968 14.01051 16.31734 11.35061 9.932025 13.77974 15.68081 16.35692 11.76693 13.50144 11.33829 10.55126 7.232647 11.33621 13.42657 9.857998 8.960086 13.31554 8.663118 13.61635 12.12258 11.96131 10.31708 10.06386 11.28873 16.27907 13.59329 4.134236 9.132328 13.81196 14.61788 11.37971 11.81842 11.9571 13.19197 12.8186 11.37996 9.118208 10.79847 12.55408 13.97338 17.03311 9.779779 8.12738 14.4028 11.12686 12.08959 12.69585 9.614664 14.55947 11.7243 13.61368 18.07005 14.11384 11.40536 8.815832 10.27914 11.20586 1.96824 3.351178 3.258677 1.938879 3.747927 4.548061 2.883941 1.550271 3.634767 2.820917 1.957743 2.512892 1.992299 2.509205 2.604609 3.400347 3.721774 2.669014 2.45143 2.952416 3.341898 3.724602 3.41813 3.360111 3.401742 3.351798 2.885793 2.054167 2.219747 3.102962 1.964199 3.541128 3.974675 4.062825 3.240341 4.34693 1.928717 2.673908 2.952996 2.810913 3.252182 1.883426 4.117749 2.896835 4.346935 3.270254 3.292605 2.044713 2.857888 3.292353 2.597607 2.901945 3.47952 1.468027 4.064165 2.348048 3.586918 7.118294 4.869135 3.483196 5.12256 3.67663 3.447801 5.671725 7.59024 3.714527 4.019361 5.389502 2.878217 5.690014 5.350924 3.784828 2.63505 3.577739 3.245812 5.554452 4.105987 3.579198 2.769982 2.94426 3.35963 4.785511 4.055522 1.432617 4.445757 6.222312 4.710944 5.793563 3.337474 3.008322 3.246996 3.955942 2.617932 4.727602 4.038461 4.251303 4.971117 5.237442 5.192546 1.973744 4.971911 2.559702 3.696837 3.855868 4.702207 5.094486 3.56107 5.240854 6.226876 4.05626 7.769171 2.169162 4.377737 3.124091 969 970 971 972 973 974 975 976 977 978 979 980 981 982 983 984 985 986 987 988 989 990 991 992 993 994 995 996 997 998 999 1000 14.01279 8.602579 8.631833 12.03892 13.94352 14.29212 13.35545 12.46686 7.165214 15.30265 13.80657 13.18473 13.50803 12.93152 15.7057 9.147544 12.51292 10.99795 16.23202 10.63472 14.32233 11.10041 7.374617 12.6189 14.09702 9.204192 12.71287 8.704286 13.01345 10.14302 13.28305 14.53436 2.363013 1.501669 3.784729 3.659223 2.511302 3.982531 3.211867 2.544286 3.103981 2.720091 2.935084 2.048613 2.781771 1.352189 2.666632 2.934527 3.149059 3.144977 2.220941 3.199159 3.317138 4.091605 3.851078 3.040348 2.653018 1.446536 2.973692 2.136927 2.879259 2.80444 2.62693 2.657855 5.930052 5.728678 2.280701 3.29002 5.552306 3.588703 4.158158 4.899944 2.308395 5.625787 4.703976 6.435927 4.85591 9.563399 5.889714 3.117212 3.973543 3.496989 7.308623 3.324222 4.317676 2.712971 1.914949 4.150478 5.31358 6.362921 4.275112 4.073273 4.519722 3.616772 5.056493 5.468457 Bin 0 1 2 3 4 5 6 7 8 9 10 11 Bin More Frequency 0 1 1 1 2 26 3 189 4 272 5 249 6 135 7 52 8 31 9 18 10 6 11 3 17 Histogram of Simulated PI Values 300 250 200 150 Frequency 100 50 0 0 1 2 3 4 5 6 Bin 7 8 9 10 11 More Expected Value Calculations Outcome, x 2 3 4 5 6 7 8 9 10 11 12 Probability, f(x) 1/36 1/18 1/12 1/ 9 5/36 1/ 6 5/36 1/ 9 1/12 1/18 1/36 Expected value x*f(x) 1/18 1/ 6 1/ 3 5/ 9 5/ 6 1 1/ 6 1 1/ 9 1 5/ 6 11/18 1/ 3 7 Variance Calculations Outcome, x 2 3 4 5 6 7 8 9 10 11 12 Probability, f(x) 1/36 1/18 1/12 1/ 9 5/36 1/ 6 5/36 1/ 9 1/12 1/18 1/36 Expected value x*f(x) (x - E[X]) (x - E[X])^2 (x - E[X])^2*f(x) 1/18 -5 25 25/36 1/ 6 -4 16 8/ 9 1/ 3 -3 9 3/ 4 5/ 9 -2 4 4/ 9 5/ 6 -1 1 5/36 1 1/ 6 0 0 0 1 1/ 9 1 1 5/36 1 2 4 4/ 9 5/ 6 3 9 3/ 4 11/18 4 16 8/ 9 1/ 3 5 25 25/36 7 Variance 5 5/ 6 Airline Passengers Sample Data 36 55 47 45 48 43 42 56 40 47 44 46 53 45 44 45 45 41 47 46 40 46 42 41 58 Bin Frequency 30.00 0 30.00 0 32.50 0 32.50 0 35.00 1 37.50 0 40.00 2 42.50 2 45.00 6 47.50 3 50.00 5 52.50 3 55.00 2 57.50 1 60.00 0 More 0 Passengers Mean Standard Error Median Mode Standard Deviation Sample Variance Kurtosis Skewness Range Minimum Maximum Sum Count 45.68 1.0435836 45 45 5.2179178 27.226667 0.7072194 0.8231631 22 36 58 1142 25 Passenger 7 6 5 4 3 Frequency 2 1 0 Passenger Demand 7 6 5 4 3 ency 2 1 0 Bin Apple Products Purchase History First Purchase iPod iPhone iMac iPhone iPod MacBook iPhone MacBook iPod MacBook MacBook iPod MacBook iPhone iPod iPod iPod MacBook iMac iMac iMac MacBook MacBook MacBook iPod iMac MacBook MacBook iPod MacBook iPhone iPod iPhone iMac iMac MacBook iPod MacBook MacBook MacBook MacBook iPod iPod MacBook iPod MacBook iPod iPod iPod MacBook Second Purchase iMac MacBook iPhone iPod iPhone iPod MacBook iPhone MacBook iPhone iMac iPhone iPod iPod MacBook MacBook MacBook iPhone iPod MacBook iPhone iPod iPod iPhone MacBook iPhone iPhone iPod MacBook iMac iPod MacBook iPod MacBook iPod iPhone iPhone iPod iPhone iPad iPod MacBook MacBook iPod iPad iPod iPhone iPhone iMac iPod MacBook MacBook iPod iPhone iPhone iPhone iPhone iPhone iPhone iPod iPhone MacBook MacBook iPhone iPhone MacBook iPod iPod MacBook iPod iPod iPod MacBook iPod iPhone iPod iPod iPod MacBook iPhone MacBook iPhone MacBook MacBook iPod iPhone iPod iPad iPod iPad MacBook iPod iPod MacBook iPod MacBook MacBook iPhone iPod iPad iPod iPhone iPod iPad iPhone iPad iPod MacBook iMac iPad iPad MacBook MacBook MacBook iPad iPad MacBook MacBook iPod iPad iMac iPhone iPhone MacBook MacBook iPhone iPad MacBook iPad iPad MacBook iPhone iPod iPod iPod iPhone iPod MacBook iPad iPhone iPhone iPhone MacBook iPhone MacBook MacBook iPhone MacBook iMac iPad MacBook MacBook MacBook MacBook iPod MacBook iPad MacBook MacBook iPad iPhone iPhone iPod iPhone MacBook iPhone iPhone iPod MacBook MacBook MacBook iPhone MacBook MacBook MacBook iPad iPod iPod MacBook iPod iMac iPhone MacBook MacBook iPod MacBook iPad iPod iMac iPod MacBook iPhone iPhone iPhone MacBook iPhone MacBook MacBook iPhone iPod iPad MacBook MacBook iPhone iPod iPod MacBook iPad iPhone MacBook iPad iPod MacBook MacBook iMac iPad iPod iPod iPod iMac iPhone iPad iMac iPhone MacBook iPhone iPod iPhone iPod iPad MacBook iPhone MacBook iPad MacBook iPod iPad MacBook iPhone iPod MacBook iPad MacBook iPod MacBook iPod MacBook iPad iPod iPad iPhone MacBook MacBook iMac iPhone iPod iPod iPhone iPad iMac MacBook MacBook MacBook iPhone MacBook iMac MacBook iPod iPod iPad MacBook iPad MacBook iPod MacBook iPod iPhone MacBook MacBook iPod iPad MacBook iPod iPhone iPod MacBook MacBook iPod MacBook MacBook MacBook iPhone iMac iPhone MacBook iPad iPhone MacBook iMac iMac MacBook iPod MacBook iPhone iPad MacBook iPad MacBook iPod MacBook iPad iPhone MacBook MacBook iMac MacBook iPhone MacBook iPhone iPad MacBook iPhone iPad iPad MacBook iPod MacBook MacBook iPhone iPod iPad iPad iMac iPod iMac MacBook MacBook iPod iPhone MacBook iPad iPad MacBook MacBook iPad MacBook iPod MacBook MacBook iPhone Sum - Second Purchase First Purchase iMac iPad iPhone iPod MacBook Total Result Second Purchase iMac iPad iPhone iPod MacBook Total Result Binomial Probabilities n p 10 0.8 x f(x) F(x) 0 0.00000 0.00000 1 0.00000 0.00000 2 0.00007 0.00008 3 0.00079 0.00086 4 0.00551 0.00637 5 0.02642 0.03279 6 0.08808 0.12087 7 0.20133 0.32220 8 0.30199 0.62419 9 0.26844 0.89263 10 0.10737 1.00000 Binomial Distribution 0.35000 0.30000 0.25000 0.20000 0.15000 0.10000 0.05000 0.00000 0 1 2 3 4 5 6 7 8 9 10 Note: for other values of n, be sure to change the data range for the chart to display the distribution correctly. Computer Repair Times Sample 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 Repair Time (Days) 18 15 17 9 37 15 8 29 10 14 17 12 13 12 11 14 13 16 13 15 16 12 34 29 13 19 12 15 16 14 15 7 40 16 11 11 10 13 14 9 18 8 13 8 10 13 16 9 9 12 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 16 9 15 17 38 11 15 16 10 9 25 15 7 11 19 13 12 20 12 13 11 8 14 10 12 15 17 10 13 18 26 14 15 12 15 9 10 21 11 36 8 20 14 18 19 14 12 16 17 12 10 10 15 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 23 13 19 19 12 13 12 16 12 14 11 14 7 16 12 16 10 12 36 9 9 22 16 12 17 9 25 14 13 13 8 14 8 17 13 12 8 12 17 22 19 10 19 10 17 13 9 13 9 11 12 17 15 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 15 27 17 10 20 15 12 15 23 17 8 17 10 20 16 12 11 22 11 14 17 18 11 21 15 14 16 10 19 14 20 27 20 15 20 11 14 13 26 9 8 15 16 21 14 15 15 14 15 15 16 5 11 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 14 8 21 10 18 13 16 11 11 10 18 11 18 23 22 19 9 11 10 6 39 14 10 11 7 13 17 8 25 20 13 21 7 12 16 23 18 31 6 17 13 Computer Repair Times Days 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 Relative Cumulative Frequency Frequency Percentage 0 0.000 0.0% 0 0.000 0.0% 0 0.000 0.0% 0 0.000 0.0% 0 0.000 0.0% 1 0.004 0.4% 2 0.008 1.2% 5 0.020 3.2% 12 0.048 8.0% 14 0.056 13.6% 19 0.076 21.2% 19 0.076 28.8% 23 0.092 38.0% 22 0.088 46.8% 20 0.080 54.8% 23 0.092 64.0% 18 0.072 71.2% 16 0.064 77.6% 9 0.036 81.2% 9 0.036 84.8% 8 0.032 88.0% 5 0.020 90.0% 4 0.016 91.6% 4 0.016 93.2% 0 0.000 93.2% 3 0.012 94.4% 2 0.008 95.2% 2 0.008 96.0% 0 0.000 96.0% 2 0.008 96.8% 0 0.000 96.8% 1 0.004 97.2% 0 0.000 97.2% 0 0.000 97.2% 1 0.004 97.6% 0 0.000 97.6% 2 0.008 98.4% 1 0.004 98.8% 1 0.004 99.2% 1 0.004 99.6% 1 0.004 100.0% 0 0.000 100.0% 0 0.000 100.0% Repair Times 25 20 15 Frequency 10 5 0 Days pair Times Days Computer Repair Times Days (x) 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 Sum Frequency (f) Frequency*Days Days - Mean (Days - mean )^2 0 0 -14.912 222.368 0 0 -13.912 193.544 0 0 -12.912 166.720 0 0 -11.912 141.896 0 0 -10.912 119.072 1 5 -9.912 98.248 2 12 -8.912 79.424 5 35 -7.912 62.600 12 96 -6.912 47.776 14 126 -5.912 34.952 19 190 -4.912 24.128 19 209 -3.912 15.304 23 276 -2.912 8.480 22 286 -1.912 3.656 20 280 -0.912 0.832 23 345 0.088 0.008 18 288 1.088 1.184 16 272 2.088 4.360 9 162 3.088 9.536 9 171 4.088 16.712 8 160 5.088 25.888 5 105 6.088 37.064 4 88 7.088 50.240 4 92 8.088 65.416 0 0 9.088 82.592 3 75 10.088 101.768 2 52 11.088 122.944 2 54 12.088 146.120 0 0 13.088 171.296 2 58 14.088 198.472 0 0 15.088 227.648 1 31 16.088 258.824 0 0 17.088 292.000 0 0 18.088 327.176 1 34 19.088 364.352 0 0 20.088 403.528 2 72 21.088 444.704 1 37 22.088 487.880 1 38 23.088 533.056 1 39 24.088 580.232 1 40 25.088 629.408 0 0 26.088 680.584 0 0 27.088 733.760 250 3728 Mean 14.912 Variance Frequency*(Days - Mean)^2 0.000 0.000 0.000 0.000 0.000 98.248 158.847 312.999 573.309 489.324 458.427 290.771 195.034 80.426 16.635 0.178 21.307 69.756 85.822 150.406 207.102 185.319 200.959 261.663 0.000 305.303 245.887 292.239 0.000 396.943 0.000 258.824 0.000 0.000 364.352 0.000 889.407 487.880 533.056 580.232 629.408 0.000 0.000 8840.064 35.5022650602 Normal Probabilities Mean Standard Deviation x 500 550 600 650 700 750 800 850 900 950 1000 750 100 F(x) 0.0062 0.0228 0.0668 0.1587 0.3085 0.5000 0.6915 0.8413 0.9332 0.9772 0.9938 Cumulative Distribution Function 1.0000 0.9000 0.8000 0.7000 0.6000 0.5000 0.4000 0.3000 0.2000 0.1000 0.0000 500 550 600 650 700 750 800 850 900 950 1000 Note: be sure the change the range of the data in the chart to display a different normal distribution properly. n 00 950 1000 PC Ownership Growth Rates Minimum Most Likely Maximum Sample 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 5% 7.70% 10% Growth Rate #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? PC Growth Rates 140 120 100 80 Frequency 60 40 20 0 0.05 0.055 0.06 0.065 0.07 0.075 0.08 0.085 0.09 0.095 0.1 More Bin 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468 469 470 471 472 473 474 475 476 477 478 479 480 481 482 483 484 485 486 487 488 489 490 491 492 493 494 495 496 497 498 499 500 #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? 9 0.095 0.1 More Bin 5% 5.50% 6% 6.50% 7% 7.50% 8% 8.50% 9% 9.50% 10% Bin Frequency 0.05 0 0.055 9 0.06 24 0.065 34 0.07 63 0.075 85 0.08 118 0.085 67 0.09 58 0.095 34 0.1 8 More 0 PC Growth Rates 140 120 100 80 Frequency 60 40 20 0 0.05 0.055 0.06 0.065 0.07 0.075 0.08 0.085 0.09 0.095 0.1 More Bin .09 0.095 0.1 More 5.24 Vehicle Driven Type Satisfaction with vehicle Gender Age # of hours per week in vehicle Miles driven per week Truck Truck Truck Truck SUV SUV SUV SUV SUV SUV SUV SUV SUV SUV SUV SUV SUV SUV SUV Mini Van Mini Van Mini Van Mini Van Mini Van Mini Van Mini Van Mini Van Mini Van Car Car Car Car Car Car Car Car Car Car Car Car Car Car Car Car Car Car Car Domestic Domestic Foreign Domestic Domestic Foreign Domestic Foreign Domestic Domestic Foreign Domestic Foreign Foreign Foreign Domestic Domestic Domestic Domestic Domestic Domestic Domestic Foreign Foreign Domestic Domestic Foreign Foreign Domestic Domestic Domestic Foreign Domestic Domestic Domestic Domestic Domestic Foreign Foreign Domestic Domestic Foreign Foreign Foreign Domestic Foreign Foreign Yes Yes No No Yes Yes Yes Yes Yes Yes Yes Yes No Yes Yes Yes No No Yes Yes No Yes Yes Yes No Yes Yes Yes Yes No Yes Yes No Yes Yes No No No Yes No Yes Yes Yes Yes Yes Yes Yes Male Male Male Male Male Male Male Male Male Male Male Male Female Female Female Male Female Female Male Female Female Female Female Female Male Female Female Female Female Female Female Male Male Female Female Male Male Female Female Female Female Female Male Male Female Female Female 31 29 26 18 49 50 48 45 45 44 41 41 39 36 33 31 31 29 28 55 43 41 38 39 35 33 32 28 21 62 61 60 58 51 47 46 44 42 41 41 39 34 33 30 29 27 26 10 5 12 6 21 16 15 5 15 10 5 30 6 4 3 10 15 4 3 8 10 10 10 15 5 10 2 8 4 5 5 5 10 11 4 4 6 5 5 10 10 10 5 5 5 6 5 450 370 580 300 1000 840 1400 300 850 700 350 1500 280 400 420 675 800 300 400 400 700 720 450 1000 350 800 200 350 150 175 355 150 600 600 300 275 285 400 350 600 700 600 400 350 250 355 175 Car Car Car Domestic Domestic Foreign No Yes No Female Female Female 24 22 19 5 5 5 300 350 500 Number of Children Average number of riders Miles from work Number of Children 0 1 0 0 0 2 3 2 0 2 1 4 1 0 0 0 1 1 1 0 2 1 4 1 2 2 4 3 0 0 0 0 0 0 0 0 2 2 2 1 1 1 1 1 0 0 0 1 1 1 1 1 1 4 2 1 1 1 3 1 1 1 1 1 1 1 2 3 2 5 2 2 3 5 4 1 2 1 1 1 1 1 1 3 3 2 2 2 2 2 2 1 2 1 30 22 15 20 22 45 25 20 25 40 20 15 17 20 25 35 50 20 15 0 0 15 0 0 0 0 5 0 0 0 15 10 35 40 21 18 16 22 23 34 45 16 22 18 19 23 11 0 1 2 3 4 COUNT TOTAL P(Fewer than three children) P(At least one child) P(Five or more children) 0 0 0 1 1 2 4 3 4 Probability Mass Cumulative Function Distribution Function hree children) 5.26 Male = 1 Female = 0 Gender Starting Age 0 18 1 18 0 19 0 19 0 19 0 19 0 19 1 19 1 19 1 19 0 20 0 20 0 20 1 20 1 20 0 21 1 21 1 21 1 21 0 22 0 22 0 23 0 23 0 23 1 23 1 23 1 23 1 24 1 24 1 24 0 25 1 25 1 25 1 25 0 26 0 26 0 26 1 26 1 26 1 27 0 28 0 28 1 29 0 30 1 30 1 30 Yes = 1 No = 0 Prior Call Center Experience 0 1 0 0 0 0 1 1 1 0 0 1 0 0 0 0 0 0 0 0 1 1 1 0 1 0 0 0 0 0 1 1 0 1 1 1 1 1 0 0 0 0 0 0 1 0 Yes = 1 No = 0 College Degree 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 1 1 1 0 1 1 0 1 1 1 1 0 0 1 1 1 0 1 Length of Service (years) 7.02 3.47 2.07 1.78 4.42 3.29 3.05 0.49 0.61 3.12 2.95 2.15 4.03 3.53 2.47 2.15 3.27 1.10 1.78 1.94 2.91 3.02 2.53 1.84 2.88 2.20 1.44 2.53 1.41 1.08 0.98 0.63 1.30 2.13 2.30 2.05 2.13 2.12 2.16 2.04 1.70 2.11 1.75 2.15 2.12 0.37 0 0 0 1 0 1 1 1 0 0 1 1 1 0 0 1 0 0 1 0 0 0 0 0 31 31 31 31 32 32 32 33 34 34 34 34 36 39 39 39 40 40 41 43 43 45 47 50 0 0 0 0 0 1 1 0 1 0 0 1 0 0 0 0 1 0 1 1 1 0 1 1 0 0 1 0 1 0 1 0 0 1 0 0 1 0 1 0 0 0 0 0 0 0 1 0 1.95 1.02 1.26 1.04 1.64 1.75 1.71 1.29 1.48 1.31 1.46 1.88 1.16 1.16 1.05 0.96 1.24 0.81 0.87 0.99 0.76 0.32 0.35 0.57 Experience 0 1 Count 43 27 Probability of Experience Probability that more than 5 of out of the 10 have experience is: 1 - P(X <=5) = use Analytic Solver Platform and place the appropriate function here. appropriate function here. 5.32 Number 0 1 2 3 4 5 6 7 8 9 10 11 12 TOTAL Empirical Probability Frequency 5 16 19 14 3 5 4 3 2 0 1 0 1 73 Mean (Expected Value): Poisson (i.e., Theoretical Probability 5.37 SAT Scores Mean S.D. 590 22 a. P(X<550) b. P(X<600) P(X<550) P(550620) d. P(X<700) P(X>700) e. Score z-scores 550 600 650 700 5.24 Vehicle Driven Type Satisfaction with vehicle Gender Age # of hours per week in vehicle Miles driven per week Truck Truck Truck Truck SUV SUV SUV SUV SUV SUV SUV SUV SUV SUV SUV SUV SUV SUV SUV Mini Van Mini Van Mini Van Mini Van Mini Van Mini Van Mini Van Mini Van Mini Van Car Car Car Car Car Car Car Car Car Car Car Car Car Car Car Car Car Car Car Domestic Domestic Foreign Domestic Domestic Foreign Domestic Foreign Domestic Domestic Foreign Domestic Foreign Foreign Foreign Domestic Domestic Domestic Domestic Domestic Domestic Domestic Foreign Foreign Domestic Domestic Foreign Foreign Domestic Domestic Domestic Foreign Domestic Domestic Domestic Domestic Domestic Foreign Foreign Domestic Domestic Foreign Foreign Foreign Domestic Foreign Foreign Yes Yes No No Yes Yes Yes Yes Yes Yes Yes Yes No Yes Yes Yes No No Yes Yes No Yes Yes Yes No Yes Yes Yes Yes No Yes Yes No Yes Yes No No No Yes No Yes Yes Yes Yes Yes Yes Yes Male Male Male Male Male Male Male Male Male Male Male Male Female Female Female Male Female Female Male Female Female Female Female Female Male Female Female Female Female Female Female Male Male Female Female Male Male Female Female Female Female Female Male Male Female Female Female 31 29 26 18 49 50 48 45 45 44 41 41 39 36 33 31 31 29 28 55 43 41 38 39 35 33 32 28 21 62 61 60 58 51 47 46 44 42 41 41 39 34 33 30 29 27 26 10 5 12 6 21 16 15 5 15 10 5 30 6 4 3 10 15 4 3 8 10 10 10 15 5 10 2 8 4 5 5 5 10 11 4 4 6 5 5 10 10 10 5 5 5 6 5 450 370 580 300 1000 840 1400 300 850 700 350 1500 280 400 420 675 800 300 400 400 700 720 450 1000 350 800 200 350 150 175 355 150 600 600 300 275 285 400 350 600 700 600 400 350 250 355 175 Car Car Car Domestic Domestic Foreign No Yes No Female Female Female 24 22 19 5 5 5 300 350 500 Number of Children Average number of riders Miles from work Number of Children 0 1 0 0 0 2 3 2 0 2 1 4 1 0 0 0 1 1 1 0 2 1 4 1 2 2 4 3 0 0 0 0 0 0 0 0 2 2 2 1 1 1 1 1 0 0 0 1 1 1 1 1 1 4 2 1 1 1 3 1 1 1 1 1 1 1 2 3 2 5 2 2 3 5 4 1 2 1 1 1 1 1 1 3 3 2 2 2 2 2 2 1 2 1 30 22 15 20 22 45 25 20 25 40 20 15 17 20 25 35 50 20 15 0 0 15 0 0 0 0 5 0 0 0 15 10 35 40 21 18 16 22 23 34 45 16 22 18 19 23 11 0 1 2 3 4 COUNT TOTAL P(Fewer than three children) P(At least one child) P(Five or more children) 0 0 0 1 1 2 4 3 4 Probability Mass Cumulative Function Distribution Function hree children) 5.26 Male = 1 Female = 0 Gender Starting Age 0 18 1 18 0 19 0 19 0 19 0 19 0 19 1 19 1 19 1 19 0 20 0 20 0 20 1 20 1 20 0 21 1 21 1 21 1 21 0 22 0 22 0 23 0 23 0 23 1 23 1 23 1 23 1 24 1 24 1 24 0 25 1 25 1 25 1 25 0 26 0 26 0 26 1 26 1 26 1 27 0 28 0 28 1 29 0 30 1 30 1 30 Yes = 1 No = 0 Prior Call Center Experience 0 1 0 0 0 0 1 1 1 0 0 1 0 0 0 0 0 0 0 0 1 1 1 0 1 0 0 0 0 0 1 1 0 1 1 1 1 1 0 0 0 0 0 0 1 0 Yes = 1 No = 0 College Degree 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 1 1 1 0 1 1 0 1 1 1 1 0 0 1 1 1 0 1 Length of Service (years) 7.02 3.47 2.07 1.78 4.42 3.29 3.05 0.49 0.61 3.12 2.95 2.15 4.03 3.53 2.47 2.15 3.27 1.10 1.78 1.94 2.91 3.02 2.53 1.84 2.88 2.20 1.44 2.53 1.41 1.08 0.98 0.63 1.30 2.13 2.30 2.05 2.13 2.12 2.16 2.04 1.70 2.11 1.75 2.15 2.12 0.37 0 0 0 1 0 1 1 1 0 0 1 1 1 0 0 1 0 0 1 0 0 0 0 0 31 31 31 31 32 32 32 33 34 34 34 34 36 39 39 39 40 40 41 43 43 45 47 50 0 0 0 0 0 1 1 0 1 0 0 1 0 0 0 0 1 0 1 1 1 0 1 1 0 0 1 0 1 0 1 0 0 1 0 0 1 0 1 0 0 0 0 0 0 0 1 0 1.95 1.02 1.26 1.04 1.64 1.75 1.71 1.29 1.48 1.31 1.46 1.88 1.16 1.16 1.05 0.96 1.24 0.81 0.87 0.99 0.76 0.32 0.35 0.57 Experience 0 1 Count 43 27 Probability of Experience Probability that more than 5 of out of the 10 have experience is: 1 - P(X <=5) = use Analytic Solver Platform and place the appropriate function here. appropriate function here. 5.32 Number 0 1 2 3 4 5 6 7 8 9 10 11 12 TOTAL Empirical Probability Frequency 5 16 19 14 3 5 4 3 2 0 1 0 1 73 Mean (Expected Value): Poisson (i.e., Theoretical Probability 5.37 SAT Scores Mean S.D. 590 22 a. P(X<550) b. P(X<600) P(X<550) P(550620) d. P(X<700) P(X>700) e. Score z-scores 550 600 650 700 5.24 Vehicle Driven Type Satisfaction with vehicle Gender Age # of hours per week in vehicle Miles driven per week Truck Truck Truck Truck SUV SUV SUV SUV SUV SUV SUV SUV SUV SUV SUV SUV SUV SUV SUV Mini Van Mini Van Mini Van Mini Van Mini Van Mini Van Mini Van Mini Van Mini Van Car Car Car Car Car Car Car Car Car Car Car Car Car Car Car Car Car Domestic Domestic Foreign Domestic Domestic Foreign Domestic Foreign Domestic Domestic Foreign Domestic Foreign Foreign Foreign Domestic Domestic Domestic Domestic Domestic Domestic Domestic Foreign Foreign Domestic Domestic Foreign Foreign Domestic Domestic Domestic Foreign Domestic Domestic Domestic Domestic Domestic Foreign Foreign Domestic Domestic Foreign Foreign Foreign Domestic Yes Yes No No Yes Yes Yes Yes Yes Yes Yes Yes No Yes Yes Yes No No Yes Yes No Yes Yes Yes No Yes Yes Yes Yes No Yes Yes No Yes Yes No No No Yes No Yes Yes Yes Yes Yes Male Male Male Male Male Male Male Male Male Male Male Male Female Female Female Male Female Female Male Female Female Female Female Female Male Female Female Female Female Female Female Male Male Female Female Male Male Female Female Female Female Female Male Male Female 31 29 26 18 49 50 48 45 45 44 41 41 39 36 33 31 31 29 28 55 43 41 38 39 35 33 32 28 21 62 61 60 58 51 47 46 44 42 41 41 39 34 33 30 29 10 5 12 6 21 16 15 5 15 10 5 30 6 4 3 10 15 4 3 8 10 10 10 15 5 10 2 8 4 5 5 5 10 11 4 4 6 5 5 10 10 10 5 5 5 450 370 580 300 1000 840 1400 300 850 700 350 1500 280 400 420 675 800 300 400 400 700 720 450 1000 350 800 200 350 150 175 355 150 600 600 300 275 285 400 350 600 700 600 400 350 250 Car Car Car Car Car Foreign Foreign Domestic Domestic Foreign Yes Yes No Yes No Female Female Female Female Female 27 26 24 22 19 6 5 5 5 5 355 175 300 350 500 Number of Children Average number of riders Miles from work Number of Children 0 1 0 0 0 2 3 2 0 2 1 4 1 0 0 0 1 1 1 0 2 1 4 1 2 2 4 3 0 0 0 0 0 0 0 0 2 2 2 1 1 1 1 1 0 1 1 1 1 1 1 4 2 1 1 1 3 1 1 1 1 1 1 1 2 3 2 5 2 2 3 5 4 1 2 1 1 1 1 1 1 3 3 2 2 2 2 2 2 1 30 22 15 20 22 45 25 20 25 40 20 15 17 20 25 35 50 20 15 0 0 15 0 0 0 0 5 0 0 0 15 10 35 40 21 18 16 22 23 34 45 16 22 18 19 0 1 2 3 4 COUNT TOTAL 23 13 9 2 3 50 P(Fewer than three children) P(At least one child) P(Five or more children) 0 0 0 0 0 2 1 1 1 2 23 11 4 3 4 Probability Mass Cumulative Function Distribution Function hree children) 0.500 0.450 0.460 0.260 0.180 0.040 0.060 0.460 0.720 0.900 0.940 1.000 0.400 0.350 0.300 Probability 0.250 0.200 0.150 0.100 0.90 0.050 - 1 2 0.54 3 Number of ch 0.00 1.200 1.000 0.800 Cumulative Probability 0.600 0.400 0.200 - 0.5 1 1.5 2 2. Numbe 0 0 0 0 0 0 0 0 0 0 bility 1 2 3 4 5 Number of children 1.200 1.000 0.800 0.600 0.400 0.200 - 0.5 1 1.5 2 2.5 3 3.5 Number of children 4 4.5 5 5.5 5.26 Male = 1 Female = 0 Gender Starting Age 0 18 1 18 0 19 0 19 0 19 0 19 0 19 1 19 1 19 1 19 0 20 0 20 0 20 1 20 1 20 0 21 1 21 1 21 1 21 0 22 0 22 0 23 0 23 0 23 1 23 1 23 1 23 1 24 1 24 1 24 0 25 1 25 1 25 1 25 0 26 0 26 0 26 1 26 1 26 1 27 0 28 0 28 1 29 0 30 Yes = 1 No = 0 Prior Call Center Experience 0 1 0 0 0 0 1 1 1 0 0 1 0 0 0 0 0 0 0 0 1 1 1 0 1 0 0 0 0 0 1 1 0 1 1 1 1 1 0 0 0 0 0 0 Yes = 1 No = 0 College Degree 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 1 1 1 0 1 1 0 1 1 1 1 0 0 1 1 1 Length of Service (years) 7.02 3.47 2.07 1.78 4.42 3.29 3.05 0.49 0.61 3.12 2.95 2.15 4.03 3.53 2.47 2.15 3.27 1.10 1.78 1.94 2.91 3.02 2.53 1.84 2.88 2.20 1.44 2.53 1.41 1.08 0.98 0.63 1.30 2.13 2.30 2.05 2.13 2.12 2.16 2.04 1.70 2.11 1.75 2.15 1 1 0 0 0 1 0 1 1 1 0 0 1 1 1 0 0 1 0 0 1 0 0 0 0 0 30 30 31 31 31 31 32 32 32 33 34 34 34 34 36 39 39 39 40 40 41 43 43 45 47 50 1 0 0 0 0 0 0 1 1 0 1 0 0 1 0 0 0 0 1 0 1 1 1 0 1 1 0 1 0 0 1 0 1 0 1 0 0 1 0 0 1 0 1 0 0 0 0 0 0 0 1 0 2.12 0.37 1.95 1.02 1.26 1.04 1.64 1.75 1.71 1.29 1.48 1.31 1.46 1.88 1.16 1.16 1.05 0.96 1.24 0.81 0.87 0.99 0.76 0.32 0.35 0.57 Experience 0 1 Probability of Experience Count 43 27 0.38571 Probability that more than 5 of out of the 10 have experience is: 1 - P(X <=5) = 0.1434 use Analytic Solver Platform and place the appropriate function here. appropriate function here. 5.32 Empirical Number 0 1 2 3 4 5 6 7 8 9 10 11 12 TOTAL Frequency 5 16 19 14 3 5 4 3 2 0 1 0 1 73 Mean (Expected Value): Probability 0.0685 0.2192 0.2603 0.1918 0.0411 0.0685 0.0548 0.0411 0.0274 0.0137 0.0137 2.96 Poisson (i.e., Theoretical Probability1 0.0519 0.1535 0.2271 0.2240 0.1657 0.0980 0.0484 0.0204 0.0076 0.0025 0.0007 0.0002 0.0000 Expected frequencies 3.7869 11.2052 16.5775 16.3504 12.0948 7.1575 3.5297 1.4920 0.5518 0.1814 0.0537 0.0144 0.0036 0.3000 Number*EP 0.2500 0.219 0.521 0.2000 0.575 0.164 Probability 0.1500 0.342 0.329 0.1000 0.288 0.219 0.0500 0.137 0.164 Empirical Probability Theoretical Probability 0 1 2 3 4 5 6 7 8 9 10 11 12 Number 5.37 SAT Scores Mean S.D. 590 22 a. P(X<550) 0.0345 b. P(X<600) P(X<550) P(550620) 0.9137 0.0863 d. P(X<700) P(X>700) 1.0000 0.0000 e. Score z-scores 550 (1.82) 600 0.45 650 2.73 700 5.00 5.24 Vehicle Driven Type Satisfaction with vehicle Gender Age # of hours per week in vehicle Miles driven per week Truck Truck Truck Truck SUV SUV SUV SUV SUV SUV SUV SUV SUV SUV SUV SUV SUV SUV SUV Mini Van Mini Van Mini Van Mini Van Mini Van Mini Van Mini Van Mini Van Mini Van Car Car Car Car Car Car Car Car Car Car Car Car Car Car Car Car Car Domestic Domestic Foreign Domestic Domestic Foreign Domestic Foreign Domestic Domestic Foreign Domestic Foreign Foreign Foreign Domestic Domestic Domestic Domestic Domestic Domestic Domestic Foreign Foreign Domestic Domestic Foreign Foreign Domestic Domestic Domestic Foreign Domestic Domestic Domestic Domestic Domestic Foreign Foreign Domestic Domestic Foreign Foreign Foreign Domestic Yes Yes No No Yes Yes Yes Yes Yes Yes Yes Yes No Yes Yes Yes No No Yes Yes No Yes Yes Yes No Yes Yes Yes Yes No Yes Yes No Yes Yes No No No Yes No Yes Yes Yes Yes Yes Male Male Male Male Male Male Male Male Male Male Male Male Female Female Female Male Female Female Male Female Female Female Female Female Male Female Female Female Female Female Female Male Male Female Female Male Male Female Female Female Female Female Male Male Female 31 29 26 18 49 50 48 45 45 44 41 41 39 36 33 31 31 29 28 55 43 41 38 39 35 33 32 28 21 62 61 60 58 51 47 46 44 42 41 41 39 34 33 30 29 10 5 12 6 21 16 15 5 15 10 5 30 6 4 3 10 15 4 3 8 10 10 10 15 5 10 2 8 4 5 5 5 10 11 4 4 6 5 5 10 10 10 5 5 5 450 370 580 300 1000 840 1400 300 850 700 350 1500 280 400 420 675 800 300 400 400 700 720 450 1000 350 800 200 350 150 175 355 150 600 600 300 275 285 400 350 600 700 600 400 350 250 Car Car Car Car Car Foreign Foreign Domestic Domestic Foreign Yes Yes No Yes No Female Female Female Female Female 27 26 24 22 19 6 5 5 5 5 355 175 300 350 500 Number of Children Average number of riders Miles from work Number of Children 0 1 0 0 0 2 3 2 0 2 1 4 1 0 0 0 1 1 1 0 2 1 4 1 2 2 4 3 0 0 0 0 0 0 0 0 2 2 2 1 1 1 1 1 0 1 1 1 1 1 1 4 2 1 1 1 3 1 1 1 1 1 1 1 2 3 2 5 2 2 3 5 4 1 2 1 1 1 1 1 1 3 3 2 2 2 2 2 2 1 30 22 15 20 22 45 25 20 25 40 20 15 17 20 25 35 50 20 15 0 0 15 0 0 0 0 5 0 0 0 15 10 35 40 21 18 16 22 23 34 45 16 22 18 19 0 1 2 3 4 COUNT TOTAL 23 13 9 2 3 50 P(Fewer than three children) P(At least one child) P(Five or more children) 0 0 0 0 0 2 1 1 1 2 23 11 4 3 4 Probability Mass Cumulative Function Distribution Function hree children) 0.500 0.450 0.460 0.260 0.180 0.040 0.060 0.460 0.720 0.900 0.940 1.000 0.400 0.350 0.300 Probability 0.250 0.200 0.150 0.100 0.90 0.050 - 1 2 0.54 3 Number of ch 0.00 1.200 1.000 0.800 Cumulative Probability 0.600 0.400 0.200 - 0.5 1 1.5 2 2. Numbe 0 0 0 0 0 0 0 0 0 0 bility 1 2 3 4 5 Number of children 1.200 1.000 0.800 0.600 0.400 0.200 - 0.5 1 1.5 2 2.5 3 3.5 Number of children 4 4.5 5 5.5 5.26 Male = 1 Female = 0 Gender Starting Age 0 18 1 18 0 19 0 19 0 19 0 19 0 19 1 19 1 19 1 19 0 20 0 20 0 20 1 20 1 20 0 21 1 21 1 21 1 21 0 22 0 22 0 23 0 23 0 23 1 23 1 23 1 23 1 24 1 24 1 24 0 25 1 25 1 25 1 25 0 26 0 26 0 26 1 26 1 26 1 27 0 28 0 28 1 29 0 30 Yes = 1 No = 0 Prior Call Center Experience 0 1 0 0 0 0 1 1 1 0 0 1 0 0 0 0 0 0 0 0 1 1 1 0 1 0 0 0 0 0 1 1 0 1 1 1 1 1 0 0 0 0 0 0 Yes = 1 No = 0 College Degree 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 1 1 1 0 1 1 0 1 1 1 1 0 0 1 1 1 Length of Service (years) 7.02 3.47 2.07 1.78 4.42 3.29 3.05 0.49 0.61 3.12 2.95 2.15 4.03 3.53 2.47 2.15 3.27 1.10 1.78 1.94 2.91 3.02 2.53 1.84 2.88 2.20 1.44 2.53 1.41 1.08 0.98 0.63 1.30 2.13 2.30 2.05 2.13 2.12 2.16 2.04 1.70 2.11 1.75 2.15 1 1 0 0 0 1 0 1 1 1 0 0 1 1 1 0 0 1 0 0 1 0 0 0 0 0 30 30 31 31 31 31 32 32 32 33 34 34 34 34 36 39 39 39 40 40 41 43 43 45 47 50 1 0 0 0 0 0 0 1 1 0 1 0 0 1 0 0 0 0 1 0 1 1 1 0 1 1 0 1 0 0 1 0 1 0 1 0 0 1 0 0 1 0 1 0 0 0 0 0 0 0 1 0 2.12 0.37 1.95 1.02 1.26 1.04 1.64 1.75 1.71 1.29 1.48 1.31 1.46 1.88 1.16 1.16 1.05 0.96 1.24 0.81 0.87 0.99 0.76 0.32 0.35 0.57 Experience 0 1 Probability of Experience Count 43 27 0.38571 Probability that more than 5 of out of the 10 have experience is: 1 - P(X <=5) = 0.1434 use Analytic Solver Platform and place the appropriate function here. appropriate function here. 5.32 Empirical Number 0 1 2 3 4 5 6 7 8 9 10 11 12 TOTAL Frequency 5 16 19 14 3 5 4 3 2 0 1 0 1 73 Mean (Expected Value): Probability 0.0685 0.2192 0.2603 0.1918 0.0411 0.0685 0.0548 0.0411 0.0274 0.0137 0.0137 2.96 Poisson (i.e., Theoretical Probability1 0.0519 0.1535 0.2271 0.2240 0.1657 0.0980 0.0484 0.0204 0.0076 0.0025 0.0007 0.0002 0.0000 Expected frequencies 3.7869 11.2052 16.5775 16.3504 12.0948 7.1575 3.5297 1.4920 0.5518 0.1814 0.0537 0.0144 0.0036 0.3000 Number*EP 0.2500 0.219 0.521 0.2000 0.575 0.164 Probability 0.1500 0.342 0.329 0.1000 0.288 0.219 0.0500 0.137 0.164 Empirical Probability Theoretical Probability 0 1 2 3 4 5 6 7 8 9 10 11 12 Number 5.37 SAT Scores Mean S.D. 590 22 a. P(X<550) 0.0345 b. P(X<600) P(X<550) P(550620) 0.9137 0.0863 d. P(X<700) P(X>700) 1.0000 0.0000 e. Score z-scores 550 (1.82) 600 0.45 650 2.73 700 5.00