Question

1. Use Appendix Table III to determine the following probabilities for the standard normal variable Z. a) P(-0.7<Z< 0.7) b) P(-1.5<Z<1.5) c) P(-2.0<Z<2.0) d) P(Z>2.0)=

Answer 1

Solection a P(-0.7 <2<0.7)=P(z<0.7 -P(ze-0.7) = 0.7500 -0.2420 = 0.516 { using z-table} P(+15<2<1:5)= P(Z <1'5 ) - P(Z <-1:5) = 0.9332- 0.0668 = 0.0664 (using z-table) O P(-2.0 <<210)= P(Z <210) - P(Z <-2.0) =0.9772 - 0 0227 = 0.9545 (using Zotable ) (dPC 2720) = 1 – P(Z < 2.0) =) - 0.9772 = 0.0228 .

7 .00 .01 .02 -3.4 .0003 ,0003 ,0003 -3.3 .0005 .0005 .0005 -3.2 .0007 .0007 .0006 -3.1 .0010 .0009 .0009 -3.0 .0013 .0013 .0013 -2.9 .0019 .0018 .0018 -2.8 .0026 .0025 .0024 -2.7 .0035 .0034 .0033 -2.6 .0047 1.0045 .004 -2.5 .0062 .0060 .0059 -2.4 20082 1.0080 .0078 -2.3 .0107 0104 .0102 -2.2 .0139 .0136 .0132 -2.1 20179 .0174 .0170 -2.0 .0228 .0222 .0217 -1.9 .0287 .0281 .0274 -1.8 .0359 .0351 .034 -1.7 .046 .0436 .0427 -1.6 .0548 .05370526 -1.5 .0668 .0655 .0643 -1.4 .0808 .0793 .0778 -1.3 0968 .0951 .0934 -1.2 1151 1131 1112 -1.1 .1357 1335 1314 -1.0 1587 .1562 1539 -0.9 1841 .1814 .1788 -0.8 .2119 12090 .2061 -0.7 .2420 .2389 .2358 -0.6 12743 ,27092676 -0.5 ,3085 13050_3015 -0.4 34634093372 -0.3 .3821 3783 .3745 -0.2 .4207 .4168 .4129 -0.1 4602 .4562 4522 -0.0 5000 .4960 .4920 .03 .04 .05 .06 .07 .08 ,0003 .0003 ,0003 ,0003 ,0003 ,0003 .0004 .0004 ,0004 ,0004 .0004 ,0004 1.0006 .0006 .0006 .0006 .0005 .0005 10009 .0008 .0008 .0008 .0008 .0007 .0012 .0012 .0011 .0011 .0011 .0010 .0017_ 0016 .0016 .0015 .0015 .0014 1.0023 .0023 .0022 .0021 .0021 .0020 20032 .0031 .0030 .0029 .0029 .0028 .0027 1.0043 .0041 .0040 .0039 .0038 .0037 20057 .0055 .0054 .0052 .0051 .0049 .0075 .0073 .0071 .0069 .0068 .0066 .0099 .0096 .0094 .0091 .0089 .0087 1.0129 .0125 20122 20119 .0116 .0113 .0166 .0162 .0158 .0154 .0150 .016 .0212 .0207 .0202 .0197 .0192 .0188 .0268 .0262 .0256 .0250 .024 .0239 .0336 .0329 .0322 .0314 ,0307 .0301 1.0418 .0409 .0401 .0392 .0384 .0375 0516 0505 .0495 .0485 .0475 10465 1.0630 .0618 .0606 .0594 .0582 .0571 1.0764 .074 .0735 .0721 .0708 .0694 .0918 .0901 ,0885 .0869 .0853 .0838 .1093 1075 1056 1038 1020 1003 .1292 1271 .1251 .1230 1210 .1190 .1515 .1492 .1469 16 .1423 .1401 .1762 1736 .1711 .1685 .1660 .1635 12033 .2005 197 1949 .1922 1894 12327 .2296 2266 .2236 2206 217 .264312611 .2578 2546.25142483 12981 129466 .2912 12877 ,2843 2810 3336 3300 3264 322831923156 370736693632 3594 35573520 1.4090 .4052 .4013 .3974 3936 3897 483 4443 4404 .4364 .4325 4286 .4880 .4840 4801 .4761 .4721 .4681 .09 ,0002 .0003 1.0005 1.0007 .0010 .0014 .0019 .0026 .0036 .0048 1.0064 .0084 20110 .0143 .0183 .0233 .0294 .0455 10559 10681 .0823 .0985 .1170 .1379 .1611 .1867 2148 | .2451 .276 3121 3483 3859 .4247 .4641

Tables of the Normal Distribution Probability Content from -00 to Z - - ---- -- -- -- - -- Zi 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 --- 0.01 0.5000 0.5040 0.5080 0.5120 0.5160 0.5199 0.5239 0.5279 0.5319 0.5359 0.1 0.5398 0.5438 0.5478 0.5517 0.5557 0.5596 0.5636 0.5675 0.5714 0.5753 0.2 0.5793 0.5832 0.5871 0.5910 0.5948 0.5987 0.6026 0.6064 0.6103 0.6141 0.3 0.6179 0.6217 0.6255 0.6293 0.6331 0.6368 0.6406 0.6443 0.6480 0.6517 0.41 0.6554 0.6591 0.6628 0.6664 0.6700 0.6736 0.6772 0.6808 0.6844 0.6879 0.5 0.6915 0.6950 0.6985 0.7019 0.7054 0.7088 0.7123 0.7157 0.7190 0.7224 0.6 0.7257 0.7291 0.7324 0.7357 0.7389 0.7422 0.7454 0.7486 0.7517 0.7549 0.71 0.7580 0.7611 0.7642 0.7673 0.7704 0.7734 0.7764 0.7794 0.7823 0.7852 0.8 0.7881 0.7910 0.7939 0.7967 0.7995 0.8023 0.8051 0.8078 0.8106 0.8133 0.9 0.8159 0.8186 0.8212 0.8238 0.8264 0.8289 0.8315 0.8340 0.8365 0.8389 1.0 | 0.8413 0.8438 0.8461 0.8485 0.8508 0.8531 0.8554 0.8577 0.8599 0.8621 1.1 0.8643 0.8665 0.8686 0.8708 0.8729 0.8749 0.8770 0.8790 0.8810 0.8830 1.2 0.8849 0.8869 0.8888 0.8907 0.8925 0.8944 0.8962 0.8980 0.8997 0.9015 1.31 0.9032 0.9049 0.9066 0.9082 0.9099 0.9115 0.9131 0.9147 0.9162 0.9177 1.4 0.9192 0.9207 0.9222 0.9236 0.9251 0.9265 0.9279 0.9292 0.9306 0.9319 1.5 0.9332 0.9345 0.9357 0.9370 0.9382 0.9394 0.9406 0.9418 0.9429 0.9441 1.6 0.9452 0.9463 0.9474 0.9484 0.9495 0.9505 0.9515 0.9525 0.9535 0.9545 1.71 0.9554 0.9564 0.9573 0.9582 0.9591 0.9599 0.9608 0.9616 0.9625 0.9633 1.8 0.9641 0.9649 0.9656 0.9664 0.9671 0.9678 0.9686 0.9693 0.9699 0.9706 1.9 0.9713 0.9719 0.9726 0.9732 0.9738 0.9744 0.9750 0.9756 0.9761 0.9767 2.0 | 0.9772 0.9778 0.9783 0.9788 0.9793 0.9798 0.9803 0.9808 0.9812 0.9817 2.1 | 0.9821 0.9826 0.9830 0.9834 0.9838 0.9842 0.9846 0.9850 0.9854 0.9857 2.21 0.9861 0.9864 0.9868 0.9871 0.9875 0.9878 0.9881 0.9884 0.9887 0.9890 2.31 0.9893 0.9896 0.9898 0.9901 0.9904 0.9906 0.9909 0.9911 0.9913 0.9916 2.4 0.9918 0.9920 0.9922 0.9925 0.9927 0.9929 0.9931 0.9932 0.9934 0.9936 2.5 0.9938 0.9940 0.9941 0.9943 0.9945 0.9946 0.9948 0.9949 0.9951 0.9952 2.6 0.9953 0.9955 0.9956 0.9957 0.9959 0.9960 0.9961 0.9962 0.9963 0.9964 2.71 0.9965 0.9966 0.9967 0.9968 0.9969 0.9970 0.9971 0.9972 0.9973 0.9974 2.8 0.9974 0.9975 0.9976 0.9977 0.9977 0.9978 0.9979 0.9979 0.9980 0.9981 2.91 0.9981 0.9982 0.9982 0.9983 0.9984 0.9984 0.9985 0.9985 0.9986 0.9986 3.0 | 0.9987 0.9987 0.9987 0.9988 0.9988 0.9989 0.9989 0.9989 0.9990 0.9990
we use above table .thank you