Problem 1 - One sample hypothesis test for mean of normal distribution (known standard deviation) A...
Fantastic news! We've Found the answer you've been seeking!
Question:
Transcribed Image Text:
Problem 1 - One sample hypothesis test for mean of normal distribution (known standard deviation) A physical therapist wished to test the mean maximal strength of a particular muscle in a certain group. He is willing to assume that maximal strength scores are approximately normally distributed with a variance of 144. A sample of 15 subjects who participated in the experiment yielded a mean of 84.3. a) Do these data provide significant evidence, at 5% significance level, that the mean maximal strength is greater than 90? i. Write the null hypothesis (Ho) and alternative hypothesis (H1) of the test. Ho: = 90 vs. H:>90 (one-sided hypothesis test of the mean) ii. Determine the cut off for rejection region and the p-value and compare the conclusions. GIVEN: = 90; n = 15; x = 84.3; = = 144 = 12; = 0.05 known - therefore we calculate z-statistic for the hypothesis test of the mean. x-Ho 84.3-90 = -1.839667 z= 12 15 The cut off for rejection region for x> , or the critical value is Z0.05 = 1.645 Since -1.8397 <1.645, we fail to reject Ho P-value: P(Z > -1.84) = P(Z < 1.84) = 0.9671 Since 0.9671> 00.5, we fail to reject Ho. Conclusion: Therefore, the experimental mean maximal muscle strength is not significantly greater than 90 at the a=0.05 significance level (z = -1.84, p = 0.967). In R, you can get the p-value using R code: pnorm(1.839667) b) Do these data provide significant evidence, at 5% significance level, that the mean maximal strength is less than 90? i. Write the null hypothesis (Ho) and alternative hypothesis (H1) of the test. Ho: = 90 vs. H1: <90 (one-sided hypothesis test of the mean) ii. Determine the cut off for rejection region and the p-value and compare the conclusions. z= x-Ho 84.3-90 = -1.839667 12 15 The cut off for rejection region for x c) Do these data provide significant evidence, at 5% significance level, that the mean maximal strength is less than or greater than 90? i. Write the null hypothesis (Ho) and alternative hypothesis (H1) of the test. Ho: = 90 vs. H1:#90 (two-sided hypothesis test of the mean) ii. Determine the cut off for rejection region and the p-value and compare the conclusions. Ho 184.3 -90 12 15 = 1.839667 The cut off for rejection region for x , or the critical value is Z-@/2 = Z0.975 = 1.96 Since |-1.8397| = 1.8397 < 1.96, we fail to reject Ho. P-value = 2 * P(Z > |1.84]) = 2 * P(Z > 1.84) = 2 * 0.0329 = 0.0658 Since 0.0658 > 0.05, we fail to reject Ho Conclusion: Therefore, the experimental mean maximal muscle strength is not significantly different from 90 at the a=0.05 significance level. A(x)=(x) = P(X x) f(x)= (-1/2)x2 (a) 0 x C(x) = Pr(0 xx) f(x)= (-1/2)x 0 x f(x)= (-1/2) B(x)=1(x) = Pr(X>x) X D(x) = Pr(-x xx) 0 x -x 0 x (c) (d) f(x) = (-1/2)x2 x A Bb C Dd x A B C D 0.0 .5000 .5000 .0 .0 0.32 .6255 .3745 .1255 .2510 0.01 .5040 .4960 .0040 .0080 0.33 .6293 .3707 .1293 .2586 0.02 .5080 .4920 .0080 .0160 0.34 .6331 .3669 .1331 .2661 0.03 .5120 .4880 .0120 .0239 0.35 .6368 .3632 .1368 .2737 0.04 .5160 .4840 .0160 .0319 0.36 .6406 .3594 .1406 .2812 0.05 .5199 .4801 .0199 .0399 0.37 .6443 .3557 .1443 .2886 0.06 .5239 .4761 .0239 .0478 0.38 .6480 .3520 .1480 .2961 0.07 .5279 .4721 .0279 .0558 0.39 .6517 .3483 .1517 .3035 0.08 .5319 .4681 .0319 .0638 0.40 .6554 .3446 .1554 .3108 0.09 .5359 .4641 .0359 .0717 0.41 .6591 .3409 .1591 .3182 0.10 .5398 .4602 .0398 .0797 0.42 .6628 .3372 .1628 .3255 0.11 .5438 .4562 .0438 .0876 0.43 .6664 .3336 .1664 .3328 0.12 .5478 .4522 .0478 .0955 0.44 .6700 .3300 .1700 .3401 0.13 .5517 .4483 .0517 .1034 0.45 .6736 .3264 .1736 .3473 0.14 .5557 .4443 .0557 .1113 0.46 .6772 .3228 .1772 .3545 0.15 .5596 .4404 .0596 .1192 0.47 .6808 .3192 .1808 .3616 0.16 .5636 .4364 .0636 .1271 0.48 .6844 .3156 .1844 .3688 0.17 .5675 .4325 .0675 .1350 0.49 .6879 .3121 .1879 .3759 0.18 .5714 .4286 .0714 .1428 0.50 .6915 .3085 .1915 .3829 0.19 .5753 .4247 .0753 .1507 0.51 .6950 .3050 .1950 .3899 0.20 .5793 .4207 .0793 .1585 0.52 .6985 .3015 .1985 .3969 0.21 .5832 .4168 .0832 .1663 0.53 .7019 .2981 .2019 .4039 0.22 .5871 .4129 .0871 .1741 0.54 .7054 .2946 .2054 .4108 0.23 .5910 .4090 .0910 .1819 0.55 .7088 .2912 .2088 .4177 0.24 .5948 .4052 .0948 .1897 0.56 .7123 .2877 .2123 .4245 0.25 .5987 .4013 .0987 .1974 0.57 .7157 .2843 .2157 .4313 0.26 .6026 .3974 .1026 .2051 0.58 .7190 .2810 .2190 .4381 0.27 .6064 .3936 .1064 .2128 0.59 .7224 .2776 .2224 .4448 0.28 .6103 .3897 .1103 .2205 0.60 .7257 .2743 .2257 .4515 0.29 .6141 .3859 .1141 .2282 0.61 .7291 .2709 .2291 .4581 0.30 .6179 .3821 .1179 .2358 0.62 .7324 .2676 .2324 .4647 0.31 .6217 .3783 .1217 .2434 0.63 .7357 .2643 .2357 .4713 A Bb C Dd A B D 0.64 .7389 2611 .2389 .4778 1.23 .8907 .1093 .3907 .7813 0.65 .7422 .2578 .2422 .4843 1.24 .8925 .1075 .3925 .7850 0.66 .7454 .2546 .2454 .4907 1.25 .8944 .1056 .3944 .7887 0.67 .7486 .2514 .2486 .4971 1.26 .8962 .1038 .3962 .7923 0.68 .7517 .2483 .2517 .5035 1.27 .8980 .1020 .3980 .7959 0.69 .7549 .2451 .2549 .5098 1.28 .8997 .1003 .3997 .7995 0.70 .7580 .2420 .2580 .5161 1.29 .9015 .0985 .4015 .8029 0.71 .7611 .2389 .2611 .5223 1.30 .9032 .0968 .4032 .8064 0.72 .7642 .2358 .2642 .5285 1.31 .9049 .0951 .4049 .8098 0.73 .7673 .2327 .2673 .5346 1.32 .9066 .0934 .4066 .8132 0.74 .7703 .2297 .2703 .5407 1.33 .9082 .0918 .4082 .8165 0.75 .7734 .2266 .2734 .5467 1.34 .9099 .0901 .4099 .8198 0.76 .7764 .2236 .2764 .5527 1.35 .9115 .0885 .4115 .8230 0.77 .7793 .2207 .2793 .5587 1.36 .9131 .0869 .4131 .8262 0.78 .7823 .2177 .2823 .5646 1.37 .9147 .0853 .4147 .8293 0.79 .7852 .2148 .2852 .5705 1.38 .9162 .0838 .4162 .8324 0.80 .7881 .2119 .2881 .5763 1.39 .9177 .0823 .4177 .8355 0.81 .7910 .2090 .2910 .5821 1.40 .9192 .0808 .4192 .8385 0.82 .7939 .2061 .2939 .5878 1.41 .9207 .0793 .4207 .8415 0.83 .7967 .2033 .2967 .5935 1.42 .9222 .0778 .4222 .8444 0.84 .7995 .2005 .2995 .5991 1.43 .9236 .0764 .4236 .8473 0.85 .8023 .1977 .3023 .6047 1.44 .9251 .0749 .4251 .8501 0.86 .8051 .1949 .3051 .6102 1.45 .9265 .0735 .4265 .8529 0.87 .8078 .1922 .3078 .6157 1.46 .9279 .0721 .4279 .8557 0.88 .8106 .1894 .3106 .6211 1.47 .9292 .0708 .4292 .8584 0.89 .8133 .1867 .3133 .6265 1.48 .9306 .0694 .4306 .8611 0.90 .8159 .1841 .3159 .6319 1.49 .9319 .0681 .4319 .8638 0.91 .8186 .1814 .3186 .6372 1.50 .9332 .0668 .4332 .8664 0.92 .8212 .1788 .3212 .6424 1.51 .9345 .0655 .4345 .8690 0.93 .8238 .1762 .3238 .6476 1.52 .9357 .0643 .4357 .8715 0.94 .8264 .1736 .3264 .6528 1.53 .9370 .0630 .4370 .8740 0.95 .8289 .1711 .3289 .6579 1.54 .9382 .0618 .4382 .8764 0.96 .8315 .1685 .3315 .6629 1.55 .9394 .0606 .4394 .8789 0.97 .8340 .1660 .3340 .6680 1.56 .9406 .0594 .4406 .8812 0.98 .8365 .1635 .3365 .6729 1.57 .9418 .0582 .4418 .8836 0.99 .8389 .1611 .3389 .6778 1.58 .9429 .0571 .4429 .8859 1.00 .8413 .1587 .3413 .6827 1.59 .9441 .0559 .4441 .8882 1.01 .8438 .1562 .3438 .6875 1.60 .9452 .0548 .4452 .8904 1.02 .8461 .1539 .3461 .6923 1.61 .9463 .0537 .4463 .8926 1.03 .8485 .1515 .3485 .6970 1.62 .9474 .0526 .4474 .8948 1.04 .8508 .1492 .3508 .7017 1.63 .9484 .0516 .4484 .8969 1.05 .8531 .1469 .3531 .7063 1.64 .9495 .0505 .4495 .8990 1.06 .8554 .1446 .3554 .7109 1.65 .9505 .0495 .4505 .9011 1.07 .8577 .1423 .3577 .7154 1.66 .9515 .0485 .4515 .9031 1.08 .8599 .1401 .3599 .7199 1.67 .9525 .0475 .4525 .9051 1.09 .8621 .1379 .3621 .7243 1.68 .9535 .0465 .4535 .9070 1.10 .8643 .1357 .3643 .7287 1.69 .9545 .0455 .4545 .9090 1.11 .8665 .1335 .3665 .7330 1.70 .9554 .0446 .4554 .9109 1.12 .8686 .1314 .3686 .7373 1.71 .9564 .0436 .4564 .9127 1.13 .8708 .1292 .3708 .7415 1.72 .9573 .0427 .4573 .9146 1.14 .8729 .1271 .3729 .7457 1.73 .9582 .0418 .4582 .9164 1.15 .8749 .1251 .3749 .7499 1.74 .9591 .0409 .4591 .9181 1.16 .8770 .1230 .3770 .7540 1.75 .9599 .0401 .4599 .9199 1.17 .8790 .1210 .3790 .7580 1.76 .9608 .0392 .4608 .9216 1.18 .8810 .1190 .3810 .7620 1.77 .9616 .0384 .4616 .9233 1.19 .8830 .1170 .3830 .7660 1.78 .9625 .0375 .4625 .9249 1.20 .8849 .1151 3849 7699 1.79 9633 .0367 4633 9265 1.20 .8849 .1151 .3849 .7699 1.79 .9633 .0367 .4633 .9265 1.21 .8869 .1131 .3869 .7737 1.80 .9641 .0359 .4641 .9281 1.22 .8888 .1112 .3888 .7775 1.81 .9649 .0351 .4649 .9297 876 APPENDIX Tables TABLE 3 The normal distribution (continued) (continued on next name) x A Bb C Dd x A B C D 1.82 .9656 .0344 .4656 .9312 2.39 .9916 .0084 .4916 .9832 1.83 .9664 .0336 .4664 .9327 2.40 .9918 .0082 .4918 .9836 1.84 .9671 .0329 .4671 .9342 2.41 .9920 .0080 .4920 .9840 1.85 .9678 .0322 .4678 .9357 2.42 .9922 .0078 .4922 .9845 1.86 .9686 .0314 .4686 .9371 2.43 .9925 .0075 .4925 .9849 1.87 .9693 .0307 .4693 .9385 2.44 .9927 .0073 .4927 .9853 1.88 .9699 .0301 .4699 .9399 2.45 .9929 .0071 .4929 .9857 1.89 .9706 .0294 .4706 .9412 2.46 .9931 .0069 .4931 .9861 1.90 .9713 .0287 .4713 .9426 2.47 .9932 .0068 .4932 .9865 1.91 .9719 .0281 .4719 .9439 2.48 .9934 .0066 .4934 .9869 1.92 .9726 .0274 .4726 .9451 2.49 .9936 .0064 .4936 .9872 1.93 .9732 .0268 .4732 .9464 2.50 .9938 .0062 .4938 .9876 1.94 .9738 .0262 .4738 .9476 2.51 .9940 .0060 .4940 .9879 1.95 .9744 .0256 .4744 .9488 2.52 .9941 .0059 .4941 .9883 1.96 .9750 .0250 .4750 .9500 2.53 .9943 .0057 .4943 .9886 1.97 .9756 .0244 .4756 .9512 2.54 .9945 .0055 .4945 .9889 1.98 .9761 .0239 .4761 .9523 2.55 .9946 .0054 .4946 .9892 1.99 .9767 .0233 .4767 .9534 2.56 .9948 .0052 .4948 .9895 2.00 .9772 .0228 .4772 .9545 2.57 .9949 .0051 .4949 .9898 2.01 .9778 .0222 .4778 .9556 2.58 .9951 .0049 .4951 .9901 2.02 .9783 .0217 .4783 .9566 2.59 .9952 .0048 .4952 .9904 2.03 .9788 .0212 .4788 .9576 2.60 .9953 .0047 .4953 .9907 2.04 .9793 .0207 .4793 .9586 2.61 .9955 .0045 .4955 .9909 2.05 .9798 .0202 .4798 .9596 2.62 .9956 .0044 .4956 .9912 2.06 .9803 .0197 .4803 .9606 2.63 .9957 .0043 .4957 .9915 2.07 .9808 .0192 .4808 .9615 2.64 .9959 .0041 .4959 .9917 2.08 .9812 .0188 .4812 .9625 2.65 .9960 .0040 .4960 .9920 2.09 .9817 .0183 .4817 .9634 2.66 .9961 .0039 .4961 .9922 2.10 .9821 .0179 .4821 .9643 2.67 .9962 .0038 .4962 .9924 2.11 .9826 .0174 .4826 .9651 2.68 .9963 .0037 .4963 .9926 2.12 .9830 .0170 .4830 .9660 2.69 .9964 .0036 .4964 .9929 2.13 .9834 .0166 .4834 .9668 2.70 .9965 .0035 .4965 .9931 2.14 .9838 .0162 .4838 .9676 2.71 .9966 .0034 .4966 .9933 2.15 .9842 .0158 .4842 .9684 2.72 .9967 .0033 .4967 .9935 2.16 .9846 .0154 .4846 .9692 2.73 .9968 .0032 .4968 .9937 2.17 .9850 .0150 .4850 .9700 2.74 .9969 .0031 .4969 .9939 2.18 .9854 .0146 .4854 .9707 2.75 .9970 .0030 .4970 .9940 2.19 .9857 .0143 .4857 .9715 2.76 .9971 .0029 .4971 .9942 2.20 .9861 .0139 .4861 .9722 2.77 .9972 .0028 .4972 .9944 2.19 .9857 .0143 .4857 .9715 2.76 .9971 .0029 .4971 .9942 2.20 .9861 .0139 .4861 .9722 2.77 .9972 .0028 .4972 .9944 2.21 .9864 .0136 .4864 .9729 2.78 .9973 .0027 .4973 .9946 2.22 .9868 .0132 .4868 .9736 2.79 .9974 .0026 .4974 .9947 2.23 .9871 .0129 .4871 .9743 2.80 .9974 .0026 .4974 .9949 2.24 .9875 .0125 .4875 .9749 2.81 .9975 .0025 .4975 .9950 2.25 .9878 .0122 .4878 .9756 2.82 .9976 .0024 .4976 .9952 2.26 .9881 .0119 .4881 .9762 2.83 .9977 .0023 .4977 .9953 2.27 .9884 .0116 .4884 .9768 2.84 .9977 .0023 .4977 .9955 2.28 .9887 .0113 .4887 .9774 2.85 .9978 .0022 .4978 .9956 2.29 .9890 .0110 .4890 .9780 2.86 .9979 .0021 .4979 .9958 2.30 .9893 .0107 .4893 .9786 2.87 .9979 .0021 .4979 .9959 2.31 .9896 .0104 .4896 .9791 2.88 .9980 .0020 .4980 .9960 2.32 .9898 .0102 .4898 .9797 2.89 .9981 .0019 .4981 .9961 2.33 .9901 .0099 .4901 .9802 2.90 .9981 .0019 .4981 .9963 2.34 .9904 .0096 .4904 .9807 2.91 .9982 .0018 .4982 .9964 2.35 .9906 .0094 .4906 .9812 2.92 .9982 .0018 .4982 .9965 2.36 .9909 .0091 .4909 .9817 2.93 .9983 .0017 .4983 .9966 2.37 .9911 .0089 .4911 .9822 2.94 .9984 .0016 .4984 .9967 2.38 .9913 .0087 .4913 .9827 2.95 .9984 .0016 .4984 .9968 Problem 1 - One sample hypothesis test for mean of normal distribution (known standard deviation) A physical therapist wished to test the mean maximal strength of a particular muscle in a certain group. He is willing to assume that maximal strength scores are approximately normally distributed with a variance of 144. A sample of 15 subjects who participated in the experiment yielded a mean of 84.3. a) Do these data provide significant evidence, at 5% significance level, that the mean maximal strength is greater than 90? i. Write the null hypothesis (Ho) and alternative hypothesis (H1) of the test. Ho: = 90 vs. H:>90 (one-sided hypothesis test of the mean) ii. Determine the cut off for rejection region and the p-value and compare the conclusions. GIVEN: = 90; n = 15; x = 84.3; = = 144 = 12; = 0.05 known - therefore we calculate z-statistic for the hypothesis test of the mean. x-Ho 84.3-90 = -1.839667 z= 12 15 The cut off for rejection region for x> , or the critical value is Z0.05 = 1.645 Since -1.8397 <1.645, we fail to reject Ho P-value: P(Z > -1.84) = P(Z < 1.84) = 0.9671 Since 0.9671> 00.5, we fail to reject Ho. Conclusion: Therefore, the experimental mean maximal muscle strength is not significantly greater than 90 at the a=0.05 significance level (z = -1.84, p = 0.967). In R, you can get the p-value using R code: pnorm(1.839667) b) Do these data provide significant evidence, at 5% significance level, that the mean maximal strength is less than 90? i. Write the null hypothesis (Ho) and alternative hypothesis (H1) of the test. Ho: = 90 vs. H1: <90 (one-sided hypothesis test of the mean) ii. Determine the cut off for rejection region and the p-value and compare the conclusions. z= x-Ho 84.3-90 = -1.839667 12 15 The cut off for rejection region for x c) Do these data provide significant evidence, at 5% significance level, that the mean maximal strength is less than or greater than 90? i. Write the null hypothesis (Ho) and alternative hypothesis (H1) of the test. Ho: = 90 vs. H1:#90 (two-sided hypothesis test of the mean) ii. Determine the cut off for rejection region and the p-value and compare the conclusions. Ho 184.3 -90 12 15 = 1.839667 The cut off for rejection region for x , or the critical value is Z-@/2 = Z0.975 = 1.96 Since |-1.8397| = 1.8397 < 1.96, we fail to reject Ho. P-value = 2 * P(Z > |1.84]) = 2 * P(Z > 1.84) = 2 * 0.0329 = 0.0658 Since 0.0658 > 0.05, we fail to reject Ho Conclusion: Therefore, the experimental mean maximal muscle strength is not significantly different from 90 at the a=0.05 significance level. A(x)=(x) = P(X x) f(x)= (-1/2)x2 (a) 0 x C(x) = Pr(0 xx) f(x)= (-1/2)x 0 x f(x)= (-1/2) B(x)=1(x) = Pr(X>x) X D(x) = Pr(-x xx) 0 x -x 0 x (c) (d) f(x) = (-1/2)x2 x A Bb C Dd x A B C D 0.0 .5000 .5000 .0 .0 0.32 .6255 .3745 .1255 .2510 0.01 .5040 .4960 .0040 .0080 0.33 .6293 .3707 .1293 .2586 0.02 .5080 .4920 .0080 .0160 0.34 .6331 .3669 .1331 .2661 0.03 .5120 .4880 .0120 .0239 0.35 .6368 .3632 .1368 .2737 0.04 .5160 .4840 .0160 .0319 0.36 .6406 .3594 .1406 .2812 0.05 .5199 .4801 .0199 .0399 0.37 .6443 .3557 .1443 .2886 0.06 .5239 .4761 .0239 .0478 0.38 .6480 .3520 .1480 .2961 0.07 .5279 .4721 .0279 .0558 0.39 .6517 .3483 .1517 .3035 0.08 .5319 .4681 .0319 .0638 0.40 .6554 .3446 .1554 .3108 0.09 .5359 .4641 .0359 .0717 0.41 .6591 .3409 .1591 .3182 0.10 .5398 .4602 .0398 .0797 0.42 .6628 .3372 .1628 .3255 0.11 .5438 .4562 .0438 .0876 0.43 .6664 .3336 .1664 .3328 0.12 .5478 .4522 .0478 .0955 0.44 .6700 .3300 .1700 .3401 0.13 .5517 .4483 .0517 .1034 0.45 .6736 .3264 .1736 .3473 0.14 .5557 .4443 .0557 .1113 0.46 .6772 .3228 .1772 .3545 0.15 .5596 .4404 .0596 .1192 0.47 .6808 .3192 .1808 .3616 0.16 .5636 .4364 .0636 .1271 0.48 .6844 .3156 .1844 .3688 0.17 .5675 .4325 .0675 .1350 0.49 .6879 .3121 .1879 .3759 0.18 .5714 .4286 .0714 .1428 0.50 .6915 .3085 .1915 .3829 0.19 .5753 .4247 .0753 .1507 0.51 .6950 .3050 .1950 .3899 0.20 .5793 .4207 .0793 .1585 0.52 .6985 .3015 .1985 .3969 0.21 .5832 .4168 .0832 .1663 0.53 .7019 .2981 .2019 .4039 0.22 .5871 .4129 .0871 .1741 0.54 .7054 .2946 .2054 .4108 0.23 .5910 .4090 .0910 .1819 0.55 .7088 .2912 .2088 .4177 0.24 .5948 .4052 .0948 .1897 0.56 .7123 .2877 .2123 .4245 0.25 .5987 .4013 .0987 .1974 0.57 .7157 .2843 .2157 .4313 0.26 .6026 .3974 .1026 .2051 0.58 .7190 .2810 .2190 .4381 0.27 .6064 .3936 .1064 .2128 0.59 .7224 .2776 .2224 .4448 0.28 .6103 .3897 .1103 .2205 0.60 .7257 .2743 .2257 .4515 0.29 .6141 .3859 .1141 .2282 0.61 .7291 .2709 .2291 .4581 0.30 .6179 .3821 .1179 .2358 0.62 .7324 .2676 .2324 .4647 0.31 .6217 .3783 .1217 .2434 0.63 .7357 .2643 .2357 .4713 A Bb C Dd A B D 0.64 .7389 2611 .2389 .4778 1.23 .8907 .1093 .3907 .7813 0.65 .7422 .2578 .2422 .4843 1.24 .8925 .1075 .3925 .7850 0.66 .7454 .2546 .2454 .4907 1.25 .8944 .1056 .3944 .7887 0.67 .7486 .2514 .2486 .4971 1.26 .8962 .1038 .3962 .7923 0.68 .7517 .2483 .2517 .5035 1.27 .8980 .1020 .3980 .7959 0.69 .7549 .2451 .2549 .5098 1.28 .8997 .1003 .3997 .7995 0.70 .7580 .2420 .2580 .5161 1.29 .9015 .0985 .4015 .8029 0.71 .7611 .2389 .2611 .5223 1.30 .9032 .0968 .4032 .8064 0.72 .7642 .2358 .2642 .5285 1.31 .9049 .0951 .4049 .8098 0.73 .7673 .2327 .2673 .5346 1.32 .9066 .0934 .4066 .8132 0.74 .7703 .2297 .2703 .5407 1.33 .9082 .0918 .4082 .8165 0.75 .7734 .2266 .2734 .5467 1.34 .9099 .0901 .4099 .8198 0.76 .7764 .2236 .2764 .5527 1.35 .9115 .0885 .4115 .8230 0.77 .7793 .2207 .2793 .5587 1.36 .9131 .0869 .4131 .8262 0.78 .7823 .2177 .2823 .5646 1.37 .9147 .0853 .4147 .8293 0.79 .7852 .2148 .2852 .5705 1.38 .9162 .0838 .4162 .8324 0.80 .7881 .2119 .2881 .5763 1.39 .9177 .0823 .4177 .8355 0.81 .7910 .2090 .2910 .5821 1.40 .9192 .0808 .4192 .8385 0.82 .7939 .2061 .2939 .5878 1.41 .9207 .0793 .4207 .8415 0.83 .7967 .2033 .2967 .5935 1.42 .9222 .0778 .4222 .8444 0.84 .7995 .2005 .2995 .5991 1.43 .9236 .0764 .4236 .8473 0.85 .8023 .1977 .3023 .6047 1.44 .9251 .0749 .4251 .8501 0.86 .8051 .1949 .3051 .6102 1.45 .9265 .0735 .4265 .8529 0.87 .8078 .1922 .3078 .6157 1.46 .9279 .0721 .4279 .8557 0.88 .8106 .1894 .3106 .6211 1.47 .9292 .0708 .4292 .8584 0.89 .8133 .1867 .3133 .6265 1.48 .9306 .0694 .4306 .8611 0.90 .8159 .1841 .3159 .6319 1.49 .9319 .0681 .4319 .8638 0.91 .8186 .1814 .3186 .6372 1.50 .9332 .0668 .4332 .8664 0.92 .8212 .1788 .3212 .6424 1.51 .9345 .0655 .4345 .8690 0.93 .8238 .1762 .3238 .6476 1.52 .9357 .0643 .4357 .8715 0.94 .8264 .1736 .3264 .6528 1.53 .9370 .0630 .4370 .8740 0.95 .8289 .1711 .3289 .6579 1.54 .9382 .0618 .4382 .8764 0.96 .8315 .1685 .3315 .6629 1.55 .9394 .0606 .4394 .8789 0.97 .8340 .1660 .3340 .6680 1.56 .9406 .0594 .4406 .8812 0.98 .8365 .1635 .3365 .6729 1.57 .9418 .0582 .4418 .8836 0.99 .8389 .1611 .3389 .6778 1.58 .9429 .0571 .4429 .8859 1.00 .8413 .1587 .3413 .6827 1.59 .9441 .0559 .4441 .8882 1.01 .8438 .1562 .3438 .6875 1.60 .9452 .0548 .4452 .8904 1.02 .8461 .1539 .3461 .6923 1.61 .9463 .0537 .4463 .8926 1.03 .8485 .1515 .3485 .6970 1.62 .9474 .0526 .4474 .8948 1.04 .8508 .1492 .3508 .7017 1.63 .9484 .0516 .4484 .8969 1.05 .8531 .1469 .3531 .7063 1.64 .9495 .0505 .4495 .8990 1.06 .8554 .1446 .3554 .7109 1.65 .9505 .0495 .4505 .9011 1.07 .8577 .1423 .3577 .7154 1.66 .9515 .0485 .4515 .9031 1.08 .8599 .1401 .3599 .7199 1.67 .9525 .0475 .4525 .9051 1.09 .8621 .1379 .3621 .7243 1.68 .9535 .0465 .4535 .9070 1.10 .8643 .1357 .3643 .7287 1.69 .9545 .0455 .4545 .9090 1.11 .8665 .1335 .3665 .7330 1.70 .9554 .0446 .4554 .9109 1.12 .8686 .1314 .3686 .7373 1.71 .9564 .0436 .4564 .9127 1.13 .8708 .1292 .3708 .7415 1.72 .9573 .0427 .4573 .9146 1.14 .8729 .1271 .3729 .7457 1.73 .9582 .0418 .4582 .9164 1.15 .8749 .1251 .3749 .7499 1.74 .9591 .0409 .4591 .9181 1.16 .8770 .1230 .3770 .7540 1.75 .9599 .0401 .4599 .9199 1.17 .8790 .1210 .3790 .7580 1.76 .9608 .0392 .4608 .9216 1.18 .8810 .1190 .3810 .7620 1.77 .9616 .0384 .4616 .9233 1.19 .8830 .1170 .3830 .7660 1.78 .9625 .0375 .4625 .9249 1.20 .8849 .1151 3849 7699 1.79 9633 .0367 4633 9265 1.20 .8849 .1151 .3849 .7699 1.79 .9633 .0367 .4633 .9265 1.21 .8869 .1131 .3869 .7737 1.80 .9641 .0359 .4641 .9281 1.22 .8888 .1112 .3888 .7775 1.81 .9649 .0351 .4649 .9297 876 APPENDIX Tables TABLE 3 The normal distribution (continued) (continued on next name) x A Bb C Dd x A B C D 1.82 .9656 .0344 .4656 .9312 2.39 .9916 .0084 .4916 .9832 1.83 .9664 .0336 .4664 .9327 2.40 .9918 .0082 .4918 .9836 1.84 .9671 .0329 .4671 .9342 2.41 .9920 .0080 .4920 .9840 1.85 .9678 .0322 .4678 .9357 2.42 .9922 .0078 .4922 .9845 1.86 .9686 .0314 .4686 .9371 2.43 .9925 .0075 .4925 .9849 1.87 .9693 .0307 .4693 .9385 2.44 .9927 .0073 .4927 .9853 1.88 .9699 .0301 .4699 .9399 2.45 .9929 .0071 .4929 .9857 1.89 .9706 .0294 .4706 .9412 2.46 .9931 .0069 .4931 .9861 1.90 .9713 .0287 .4713 .9426 2.47 .9932 .0068 .4932 .9865 1.91 .9719 .0281 .4719 .9439 2.48 .9934 .0066 .4934 .9869 1.92 .9726 .0274 .4726 .9451 2.49 .9936 .0064 .4936 .9872 1.93 .9732 .0268 .4732 .9464 2.50 .9938 .0062 .4938 .9876 1.94 .9738 .0262 .4738 .9476 2.51 .9940 .0060 .4940 .9879 1.95 .9744 .0256 .4744 .9488 2.52 .9941 .0059 .4941 .9883 1.96 .9750 .0250 .4750 .9500 2.53 .9943 .0057 .4943 .9886 1.97 .9756 .0244 .4756 .9512 2.54 .9945 .0055 .4945 .9889 1.98 .9761 .0239 .4761 .9523 2.55 .9946 .0054 .4946 .9892 1.99 .9767 .0233 .4767 .9534 2.56 .9948 .0052 .4948 .9895 2.00 .9772 .0228 .4772 .9545 2.57 .9949 .0051 .4949 .9898 2.01 .9778 .0222 .4778 .9556 2.58 .9951 .0049 .4951 .9901 2.02 .9783 .0217 .4783 .9566 2.59 .9952 .0048 .4952 .9904 2.03 .9788 .0212 .4788 .9576 2.60 .9953 .0047 .4953 .9907 2.04 .9793 .0207 .4793 .9586 2.61 .9955 .0045 .4955 .9909 2.05 .9798 .0202 .4798 .9596 2.62 .9956 .0044 .4956 .9912 2.06 .9803 .0197 .4803 .9606 2.63 .9957 .0043 .4957 .9915 2.07 .9808 .0192 .4808 .9615 2.64 .9959 .0041 .4959 .9917 2.08 .9812 .0188 .4812 .9625 2.65 .9960 .0040 .4960 .9920 2.09 .9817 .0183 .4817 .9634 2.66 .9961 .0039 .4961 .9922 2.10 .9821 .0179 .4821 .9643 2.67 .9962 .0038 .4962 .9924 2.11 .9826 .0174 .4826 .9651 2.68 .9963 .0037 .4963 .9926 2.12 .9830 .0170 .4830 .9660 2.69 .9964 .0036 .4964 .9929 2.13 .9834 .0166 .4834 .9668 2.70 .9965 .0035 .4965 .9931 2.14 .9838 .0162 .4838 .9676 2.71 .9966 .0034 .4966 .9933 2.15 .9842 .0158 .4842 .9684 2.72 .9967 .0033 .4967 .9935 2.16 .9846 .0154 .4846 .9692 2.73 .9968 .0032 .4968 .9937 2.17 .9850 .0150 .4850 .9700 2.74 .9969 .0031 .4969 .9939 2.18 .9854 .0146 .4854 .9707 2.75 .9970 .0030 .4970 .9940 2.19 .9857 .0143 .4857 .9715 2.76 .9971 .0029 .4971 .9942 2.20 .9861 .0139 .4861 .9722 2.77 .9972 .0028 .4972 .9944 2.19 .9857 .0143 .4857 .9715 2.76 .9971 .0029 .4971 .9942 2.20 .9861 .0139 .4861 .9722 2.77 .9972 .0028 .4972 .9944 2.21 .9864 .0136 .4864 .9729 2.78 .9973 .0027 .4973 .9946 2.22 .9868 .0132 .4868 .9736 2.79 .9974 .0026 .4974 .9947 2.23 .9871 .0129 .4871 .9743 2.80 .9974 .0026 .4974 .9949 2.24 .9875 .0125 .4875 .9749 2.81 .9975 .0025 .4975 .9950 2.25 .9878 .0122 .4878 .9756 2.82 .9976 .0024 .4976 .9952 2.26 .9881 .0119 .4881 .9762 2.83 .9977 .0023 .4977 .9953 2.27 .9884 .0116 .4884 .9768 2.84 .9977 .0023 .4977 .9955 2.28 .9887 .0113 .4887 .9774 2.85 .9978 .0022 .4978 .9956 2.29 .9890 .0110 .4890 .9780 2.86 .9979 .0021 .4979 .9958 2.30 .9893 .0107 .4893 .9786 2.87 .9979 .0021 .4979 .9959 2.31 .9896 .0104 .4896 .9791 2.88 .9980 .0020 .4980 .9960 2.32 .9898 .0102 .4898 .9797 2.89 .9981 .0019 .4981 .9961 2.33 .9901 .0099 .4901 .9802 2.90 .9981 .0019 .4981 .9963 2.34 .9904 .0096 .4904 .9807 2.91 .9982 .0018 .4982 .9964 2.35 .9906 .0094 .4906 .9812 2.92 .9982 .0018 .4982 .9965 2.36 .9909 .0091 .4909 .9817 2.93 .9983 .0017 .4983 .9966 2.37 .9911 .0089 .4911 .9822 2.94 .9984 .0016 .4984 .9967 2.38 .9913 .0087 .4913 .9827 2.95 .9984 .0016 .4984 .9968
Expert Answer:
Posted Date:
Students also viewed these mathematics questions
-
Jane Grimes, retail fruit and vegetable merchant, does not keep a full set of accounting records. However, the following information has been produced from the business's records: 1. Summary of the...
-
What is the primary source of information for preparing the financial statements?
-
Determine the required heat-transfer surface area for a heat exchanger constructed from 10-cm OD tubes. A 95% ethanol solution (c p = 3.8l0kJ/kg K), flowing at 6.93 kg/s is cooled from 340 to 312 K...
-
Identify the accounting assumption, principle, or constraint that best describes the accounting practices at Ben Wallace Company. 1. Land is valued at its original purchase price rather than its...
-
A large distributor of oil-well drilling equipment operated over the past two years with EOQ policies based on an annual holding cost rate of 22%. Under the EOQ policy, a particular product has been...
-
An object is to move along an x axis from x = 0 to X1 while a conservative force, directed along the x axis, acts on the object. The figure shows three cases, each of which the force varies with x...
-
(10 pts) An aluminum "L" shaped bar (also known as "angle") and its cross-section are shown in the fol- lowing figure. Hand-calculate the centroid of the section and the moments inertia, Ir and Iy,...
-
15. Using the Truth Tables below, demonstrate that the Boolean Expression (on the left) is equal to the Boolean Expression (on the right). 6pts. A+AB=A+B A 0 0 1 1 B 0 1 0 1 A AB 16. Convert the...
-
Upload your response as a word or pdf file using the 'Browse My Computer' button below. You manage an investment portfolio which has an acquisition mandate. For any new acquisitions to meet board...
-
Ferdinand Construction (FC) manages the design and construction of hospitals. Ferdinand has developed several formulas that it uses to quote jobs. These include costs of basic construction but...
-
Christopher's Custom Cabinet Company uses a job order cost system with overhead applied as a percentage of direct labor costs. Inventory balances at the beginning of the current year follow: Raw...
-
Company is considering outsourcing a key component. A reliable supplier has quoted a price of $65.50 per unit. The following costs of the component when manufactured in-house are expressed on a per...
-
Which of the following are concepts or terms relevant to the discipline of disaster recovery? [Choose all that apply.] A. Backup policies B. Backup execution C. Warm site Backup frequency D. Cold...
-
Suppose that you could invest in the following projects but have only $30,000 to invest. How would you make your decision and which projects would you invest in? Project Cost $ 8,000 11,000 9,000...
Study smarter with the SolutionInn App