TABLE 1 Standard Normal Curve Areas Entries in this table provide cumulative probabilities, that is, the area under the curve to the left of -z. For example, P(Z -1.52) = 0.0643. Z -3.9 -3.8 -3.7 0.00 0.01 0.0000 0.0000 0.0001 0.0001 0.0001 0.0001 -3.6 -3.5 -3.4 -3.3 -3.2 -3.1 -3.0 -2.9 -2.8 -2.7 -2.6 0.02 0.03 0.04 0.0000 0.0000 0.0000 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0002 0.0002 0.0001 0.0001 0.0001 0.0002 0.0002 0.0002 0.0003 0.0003 0.0003 0.0005 0.05 0.0001 0.0002 0.0002 0.0002 0.0003 0.0005 0.0005 0.0004 0.0003 0.0003 0.0004 0.0004 0.0007 0.0007 0.0006 0.0006 0.0006 0.0006 0.0010 0.0009 0.0009 0.0009 0.0008 0.0008 0.0008 0.06 0.07 0.08 0.0000 0.0000 0.0000 0.0000 0.0000 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0002 0.0002 0.0003 0.0003 0.0003 0.0002 0.0004 0.0004 0.0004 0.0003 0.0006 0.0005 0.0005 0.0005 0.0008 0.09 0.0002 0.0002 0.0007 0.0007 -2.5 0.0013 0.0013 0.0013 0.0019 0.0018 0.0018 0.0026 0.0025 0.0024 0.0035 0.0034 0.0033 0.0047 0.0045 0.0044 0.0062 0.0060 0.0012 0.0012 0.0011 0.0011 0.0011 0.0043 0.0017 0.0016 0.0016 0.0015 0.0023 0.0023 0.0022 0.0021 0.0032 0.0031 0.0030 0.0029 0.0041 0.0040 0.0021 0.0010 0.0010 0.0015 0.0014 0.0014 0.0020 0.0019 0.0028 0.0027 0.0026 0.0039 0.0038 0.0037 0.0036 0.0059 0.0057 0.0055 0.0054 0.0052 0.0051 0.0049 0.0048 -2.4 0.0082 0.0080 0.0078 0.0075 0.0073 0.0071 0.0069 0.0068 0.0066 0.0064 -2.3 0.0107 0.0104 0.0102 0.0099 0.0096 0.0094 0.0091 -2.2 0.0139 0.0136 0.0132 0.0129 0.0125 0.0122 0.0119 -2.1 0.0179 -2.0 0.0228 -1.9 -1.8 -1.7 -1.6 -1.5 -1.4 -1.3 -1.2 -1.1 -1.0 -0.9 -0.8 -0.7 -0.6 -0.5 -0.4 -0.3 -0.2 -0.1 -0.0 0.0174 0.0170 0.0166 0.0162 0.0222 0.0217 0.0212 0.0207 0.0197 0.0287 0.0281 0.0274 0.0268 0.0262 0.0256 0.0250 0.0359 0.0351 0.0344 0.0336 0.0329 0.0322 0.0314 0.0446 0.0436 0.0427 0.0418 0.0409 0.0401 0.0392 0.0548 0.0537 0.0526 0.0516 0.0505 0.0495 0.0485 0.0668 0.0655 0.0643 0.0630 0.0618 0.0606 0.0594 0.0808 0.0793 0.0778 0.0764 0.0749 0.0735 0.0721 0.0968 0.0951 0.0934 0.0918 0.0901 0.0885 0.0869 0.1151 0.1131 0.1112 0.1093 0.1075 0.1056 0.1038 0.1357 0.1335 0.1314 0.1292 0.1271 0.1251 0.1230 0.1587 0.1562 0.1539 0.1515 0.1492 0.1469 0.1446 0.1841 0.1814 0.1788 0.1762 0.1736 0.1711 0.1685 0.2119 0.2090 0.2061 0.2033 0.2005 0.1977 0.1949 0.2420 0.2389 0.2358 0.2327 0.2296 0.2266 0.2236 0.2743 0.2709 0.2676 0.2643 0.2611 0.2578 0.2546 0.3085 0.3050 0.3015 0.2981 0.2946 0.2912 0.2877 0.3446 0.3409 0.3372 0.3336 0.3300 0.3228 0.3821 0.3783 0.3745 0.3707 0.3669 0.3594 0.4207 0.4168 0.4129 0.4090 0.4052 0.4602 0.4562 0.4522 0.4483 0.4443 0.5000 0.4960 0.4920 0.4880 0.4840 0.0158 0.0154 0.0202 0.0089 0.0116 0.0113 0.0110 0.0150 0.0146 0.0143 0.0192 0.0188 0.0183 0.0244 0.0239 0.0233 0.0307 0.0301 0.0294 0.0384 0.0375 0.0367 0.0475 0.0465 0.0455 0.0582 0.0571 0.0559 0.0708 0.0694 0.0681 0.0853 0.0838 0.0823 0.1020 0.1003 0.0985 0.1210 0.0087 0.0084 0.1190 0.1170 0.1423 0.1401 0.1379 0.1660 0.1635 0.1611 0.1922 0.1894 0.1867 0.2206 0.2177 0.2148 0.3264 0.3632 0.2514 0.2843 0.3192 0.3156 0.3557 0.2483 0.2451 0.2810 0.2776 0.3121 0.3520 0.3483 0.4013 0.4404 0.4364 0.4801 0.4761 0.3974 0.3936 0.3897 0.3859 0.4325 0.4286 0.4247 0.4721 0.4681 0.4641 Source: Probabilities calculated with Excel. TABLE 1 (Continued) Entries in this table provide cumulative probabilities, that is, the area under the curve to the left of z. For example, P(Z 1.52) = 0.9357. N 0.0 0.00 0.01 0.02 0.5000 0.5040 0.5080 0.1 0.5398 0.5438 0.5478 0.03 0.5120 0.5517 0.04 0.5160 0.5557 0.2 0.5793 0.5832 0.5871 0.5910 0.5948 0.3 0.6179 0.6217 0.6255 0.6293 0.6331 0.4 0.6554 0.6591 0.6628 0.6664 0.6700 0.5 0.6915 0.6950 0.6985 0.6 0.7 0.8 0.9 1.0 1.1 0.8708 0.8729 1.2 0.8907 0.8925 1.3 0.9082 0.9099 1.4 0.9251 1.5 1.6 1.7 1.8 1.9 2.0 2.1 2.2 2.3 0.9861 0.9864 0.9868 0.9893 0.9896 0.9898 2.4 0.9918 2.5 0.9920 0.9922 0.9938 0.9940 0.9941 0.9332 0.9345 0.9357 0.9452 0.9463 0.9474 0.9554 0.9564 0.9573 0.9641 0.9649 0.9656 0.9664 0.9671 0.9713 0.9719 0.9726 0.9732 0.9738 0.9772 0.9778 0.9783 0.9788 0.9793 0.9821 0.9826 0.9830 0.9834 0.9838 0.9871 0.9875 0.9901 0.9904 0.9925 0.9927 0.9382 0.05 0.06 0.07 0.09 0.5199 0.5239 0.5279 0.5319 0.5359 0.5596 0.5636 0.5675 0.5714 0.5753 0.5987 0.6026 0.6064 0.6103 0.6141 0.6368 0.6406 0.6443 0.6480 0.6517 0.6736 0.6772 0.6808 0.6844 0.6879 0.7019 0.7054 0.7088 0.7123 0.7157 0.7190 0.7224 0.7257 0.7291 0.7324 0.7357 0.7389 0.7422 0.7454 0.7486 0.7517 0.7549 0.7580 0.7611 0.7642 0.7673 0.7704 0.7734 0.7764 0.7794 0.7823 0.7852 0.7881 0.7910 0.7939 0.7967 0.7995 0.8023 0.8051 0.8078 0.8106 0.8133 0.8159 0.8186 0.8212 0.8238 0.8264 0.8289 0.8315 0.8340 0.8365 0.8389 0.8413 0.8438 0.8461 0.8485 0.8508 0.8531 0.8554 0.8577 0.8599 0.8621 0.8643 0.8665 0.8686 0.8849 0.8869 0.8888 0.9032 0.9049 0.9066 0.9192 0.9207 0.9222 0.9236 0.9370 0.08 0.8749 0.8770 0.8790 0.8810 0.8830 0.8944 0.8962 0.8980 0.8997 0.9015 0.9115 0.9131 0.9147 0.9162 0.9177 0.9265 0.9279 0.9394 0.9406 0.9484 0.9495 0.9505 0.9515 0.9582 0.9591 0.9599 0.9608 0.9678 0.9686 0.9292 0.9306 0.9319 0.9418 0.9429 0.9441 0.9525 0.9535 0.9545 0.9616 0.9693 0.9625 0.9633 0.9744 0.9750 0.9699 0.9706 0.9756 0.9761 0.9767 0.9929 0.9798 0.9803 0.9842 0.9846 0.9878 0.9881 0.9906 0.9909 0.9931 0.9932 0.9808 0.9812 0.9817 0.9850 0.9854 0.9857 0.9884 0.9911 0.9887 0.9890 0.9913 0.9916 0.9943 0.9945 0.9946 0.9948 0.9949 0.9934 0.9936 0.9951 0.9952 2.6 2.7 2.8 0.9953 0.9955 0.9956 0.9957 0.9965 0.9966 0.9967 0.9974 0.9975 0.9976 0.9977 0.9959 0.9960 0.9961 0.9962 0.9963 0.9964 0.9968 0.9969 0.9970 0.9971 0.9972 0.9973 0.9974 0.9977 0.9978 0.9979 0.9979 0.9980 0.9981 2.9 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 3.1 3.2 3.3 0.9990 0.9991 0.9991 0.9991 0.9992 0.9993 0.9993 0.9994 0.9994 0.9994 0.9995 0.9995 0.9995 0.9996 0.9996 3.4 3.5 0.9997 0.9998 0.9997 0.9997 0.9997 0.9997 0.9998 0.9998 3.6 0.9998 0.9998 0.9998 0.9999 0.9999 3.7 3.8 3.9 0.9999 0.9999 1.0000 0.9992 0.9992 0.9992 0.9994 0.9994 0.9995 0.9996 0.9996 0.9996 0.9996 0.9997 0.9997 0.9997 0.9997 0.9997 0.9998 0.9998 0.9998 0.9998 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9993 0.9993 0.9995 0.9995 0.9998 0.9998 0.9998 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 1.0000 1.0000 1.0000 Source: Probabilities calculated with Excel. It is well documented that a typical washing machine can last anywhere between 5 to 20 years. Let the life of a washing machine be represented by a lognormal variable, Y = ex where X is normally distributed. In addition, let the mean and standard deviation of the life of a washing machine be 10 and half years and 3 years, respectively. [You may find it useful to reference the z table.] a. Compute the mean and the standard deviation of X. (Round your intermediate calculations to at least 4 decimal places and final answers to 4 decimal places.) Mean Standard deviation b. What proportion of the washing machines will last for more than 12 years? (Round your intermediate calculations to at least 4 decimal places and final answer to 4 decimal places.) Proportion c. What proportion of the washing machines will last for less than 9 years? (Round your intermediate calculations to at least 4 decimal places and final answer to 4 decimal places.) Proportion d. Compute the 60th percentile of the life of the washing machines. (Round your intermediate calculations to at least 4 decimal places and final answer to the nearest whole number.) The 60th percentile