Practice FT2 Q2 - Looking for a detailed, worked solution with theoretical explanation

Let Z be a standard normal random variable. Find the probability that Z 4: 2.42 given mat Z > 1.42. Give your answer to four deicmal places, such as U .1234 P(Z 1.42) = | Number | _ Standard normal probabilities P(Z g z) I 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.0? 0.08 0.09 -2.9 0.0019 0.0018 0.0018 0.001? 0.0015 0.0015 0.0015 0.0015 0.0014 0.0014 -2.8 0.0025 0.0025 0.0024 0.0023 0.0023 0.0022 0.0021 0.0021 0.0020 0.0019 -2.? 0.0035 0.0034 0.0033 0.0032 0.0031 0.0030 0.0029 0.0028 0.002? 0.0025 -2.6 0.004? 0.0045 0.0044 0.0043 0.0041 0.0040 0.0039 0.0038 0.003? 0.0035 -2.5 0.0052 0.0050 0.0059 0.005? 0.0055 0.0054 0.0052 0.0051 0.0049 0.0048 -2.4 0.0082 0.0080 0.00?8 0.00?5 0.00?3 0.00?1 0.0059 0.0058 0.0055 0.0054 -2.3 0.010? 0.0104 0.0102 0.0099 0.0095 0.0094 0.0091 0.0089 0.008? 0.0084 -2.2 0.0139 0.0135 0.0132 0.0129 0.0125 0.0122 0.0119 0.0115 0.0113 0.0110 -2.1 0.01?9 0.01?4 0.01?0 0.0155 0.0152 0.0158 0.0154 0.0150 0.0145 0.0143 -2.(1 0.0228 0.0222 0.021? 0.0212 0.020? 0.0202 0.019? 0.0192 0.0188 0.0183 -1.9 0.028? 0.0281 0.02?4 0.0258 0.0252 0.0255 0.0250 0.0244 0.0239 0.0233 -1.8 0.0359 0.0352 0.0344 0.0335 0.0329 0.0322 0.0314 0.030? 0.0301 0.0294 -1.? 0.0445 0.0435 0.042? 0.0418 0.0409 0.0401 0.0392 0.0384 0.03?5 0.035? -1.6 0.0548 0.053? 0.0525 0.0515 0.0505 0.0495 0.0485 0.04?5 0.0455 0.0455 -1.5 0.0658 0.0655 0.0643 0.0630 0.0618 0.0605 0.0594 0.0582 0.05?1 0.0559 -1.4 0.0808 0.0?93 0.0??8 0.0?54 0.0?49 0.0?35 0.0?22 0.0?08 0.0694 0.0681 -1.3 0.0958 0.0951 0.0934 0.0918 0.0901 0.0885 0.0859 0.0853 0.0838 0.0823 -1.2 0.1151 0.1131 0.1112 0.1093 0.10?5 0.1055 0.1038 0.1020 0.1003 0.0985 -1.1 0.135? 0.1335 0.1314 0.1292 0.12?1 0.1251 0.1230 0.1210 0.1190 0.11?0 -1.(1 0.158? 0.1552 0.1539 0.1515 0.1492 0.1459 0.1445 0.1423 0.1401 0.13?9 41.9 0.1841 0.1814 0.1?88 0.1?52 0.1?35 0.1?11 0.1685 0.1650 0.1635 0.1611 41.8 0.2119 0.2090 0.2051 0.2033 0.2005 0.19?? 0.1949 0.1922 0.1894 0.185? 41.? 0.2420 0.2389 0.2358 0.232? 0.2295 0.2255 0.2235 0.2205 021?? 0.2148 41.6 0.2?43 0.2?09 0.26?5 0.2643 0.2611 0.25?8 0.2545 0.2514 0.2483 0.2451 41.5 0.3085 0.3050 0.3015 0.2981 0.2945 0.2912 028?? 0.2843 0.2810 0.2??5 41.4 0.3445 0.3409 0.33?2 0.3335 0.3300 0.3254 0.3228 0.3192 0.3155 0.3121 41.3 0.3821 0.3?83 0.3?45 0.3?0? 0.3659 0.3632 0.3594 0.355? 0.3520 0.3483 41.2 0.420? 0.4158 0.4129 0.4090 0.4052 0.4013 0.39?4 0.3935 0.389? 0.3859 41.1 0.4602 0.4552 0.4522 0.4483 0.4443 0.4404 0.4354 0.4325 0.4285 0.424? 41.0 0.5000 0.4950 0.4920 0.4880 0.4840 0.4801 0.4?51 0.4?21 0.4681 0.4641 0.0 0.5000 0.5040 0.5080 0.5120 0.5150 0.5199 0.5239 0.52?9 0.5319 0.5359 0.1 0.5398 0.5438 0.54?8 0.551? 0.555? 0.5595 0.5635 0.56?5 0.5?14 0.5?53 0.2 0.5?93 0.5832 0.58?1 0.5910 0.5948 0.598? 0.6025 0.6054 0.6103 0.6141 0.3 0.61?9 0.621? 0.6255 0.6293 0.6331 0.6358 0.6405 0.6443 0.6480 0.651? 0.4 0.6554 0.6591 0.6628 0.6654 0.6?00 0.6?35 0.6??2 0.6808 0.6844 0.68?9 0.5 0.6915 0.6950 0.6985 0.?019 0.?054 0.?088 0.?123 0.?15? 0.?190 0.?224 0.6 0.?25? 0.?291 0.?324 0.?35? 0.?389 0.?422 0.?454 0.?485 0.?51? 0.?549 0.? 0.?580 0.?611 0.?642 0.?6?3 0.??04 0.??34 0.??54 0.??94 0.?823 0.?852 0.8 0.?881 0.?910 0.?939 0.?95? 0.?995 0.8023 0.8051 0.80?8 0.8105 0.8133 0.9 0.8159 0.8185 0.8212 0.8238 0.8254 0.8289 0.8315 0.8340 0.8355 0.8389 1.0 0.8413 0.8438 0.8451 0.8485 0.8508 0.8531 0.8554 0.85?? 0.8599 0.8621 1.1 0.8643 0.8655 0.8685 0.8?08 0.8?29 0.8?49 0.8??0 0.8?90 0.8810 0.8830 1.2 0.8849 0.8859 0.8888 0.890? 0.8925 0.8944 0.8952 0.8980 0.899? 0.9015 1.3 0.9032 0.9049 0.9055 0.9082 0.9099 0.9115 0.9131 0.914? 0.9152 0.91?? 1.4 0.9192 0.920? 0.9222 0.9235 0.9251 0.9255 0.92?9 0.9292 0.9305 0.9319 1.5 0.9332 0.9345 0.935? 0.93?0 0.9382 0.9394 0.9405 0.9418 0.9429 0.9441 1.6 0.9452 0.9453 0.94?4 0.9484 0.9495 0.9505 0.9515 0.9525 0.9535 0.9545 1.? 0.9554 0.9554 0.95?3 0.9582 0.9591 0.9599 0.9608 0.9615 0.9625 0.9633 1.8 0.9641 0.9649 0.9655 0.9654 0.96?1 0.96?8 0.9685 0.9693 0.9699 0.9?05 1.9 0.9?13 0.9?19 0.9?25 0.9?32 0.9?38 0.9?44 0.9?50 0.9?55 0.9?51 0.9?5? 2.0 0.9??2 0.9??8 0.9?83 0.9?88 0.9?93 0.9?98 0.9803 0.9808 0.9812 0.981? 2.1 0.9821 0.9825 0.9830 0.9834 0.9838 0.9842 0.9845 0.9850 0.9854 0.985? 2.2 0.9851 0.9854 0.9858 0.98?1 0.98?5 0.98?8 0.9881 0.9884 0.988? 0.9890 2.3 0.9893 0.9895 0.9898 0.9901 0.9904 0.9905 0.9909 0.9911 0.9913 0.9915 2.4 0.9918 0.9920 0.9922 0.9925 0.992? 0.9929 0.9931 0.9932 0.9934 0.9935 2.5 0.9938 0.9940 0.9941 0.9943 0.9945 0.9945 0.9948 0.9949 0.9951 0.9952 2.6 0.9953 0.9955 0.9955 0.995? 0.9959 0.9950 0.9951 0.9952 0.9953 0.9954 2.? 0.9955 0.9955 0.995? 0.9958 0.9959 0.99?0 0.99?1 0.99?2 0.99?3 0.99?4 2.8 0.99?4 0.99?5 0.99?5 0.99?? 0.99?? 0.99?8 0.99?9 0.99?9 0.9980 0.9981 2.9 0.9981 0.9982 0.9982 0.9983 0.9984 0.9984 0.9985 0.9985 0.9985 0.9985