Exercise 6-40 Algo

The time required to assemble an electronic component is normally distributed with a mean and a standard deviation of 34 minutes and 14 minutes, respectively. [You may find it useful to reference the z table.] a. Find the probability that a randomly picked assembly takes between 16 and 40 minutes. (Round your final answer to 4 decimal places.)

b. It is unusual for the assembly time to be above 48 minutes or below 16 minutes. What proportion of assembly times fall in these unusual categories? (Round your final answer to 4 decimal places.)

TABLE 1 Standard Normal Curve Areas Entries in this table provide cumulative probabilities, that is, the area P (ZS - 2) under the curve to the left of -z. For example, P(Z S -1.52) = 0.0643. -Z 0 Z 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.0000 0.0000 0.0000 0.0000 -3.9 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0001 -3.8 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 0.0001 0.0001 0.0001 -3.7 0.0001 0.0001 0.0002 0.0002 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 -3.6 -3.5 0.0002 0.0002 0.0002 0.0002 0.0002 0.0002 0.0002 0.0002 0.0002 0.0002 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.0002 -3. 0.0005 0.0004 0.0004 0.0004 0.0003 -3.3 0.0005 0.0005 0.0004 0.0004 0.0004 0.0007 0.0007 0.0006 0.0006 0.0006 0.0006 0.0006 0.0005 0.0005 0.0005 -3.2 0.0010 0.0009 0.0009 0.0009 0.0008 0.0008 0.0008 0.0008 0.0007 0.0007 -3.1 0.0012 0.0010 0.0013 0.0013 0.0011 0.0011 0.0010 -3.0 0.0013 0.0012 0.0011 0.0014 0.0014 -2.9 0.0019 0.0018 0.0018 0.0017 0.0016 0.0016 0.0015 0.0015 -2.8 0.0026 0.0025 0.0024 0.0023 0.0023 0.0022 0.0021 0.0021 0.0020 0.0019 0.0028 0.0027 0.0026 -2.7 0.0035 0.0034 0.0033 0.0032 0.0031 0.0030 0.0029 0.0038 0.0037 0.0036 -2.6 0.0047 0.0045 0.0044 0.0043 0.0041 0.0040 0.0039 0.0049 0.0048 -2.5 0.0062 0.0060 0.0059 0.0057 0.0055 0.0054 0.0052 0.0051 0.0069 0.0068 0.0066 0.0064 -2.4 0.0082 0.0080 0.0078 0.0075 0.0073 0.0071 0.0102 0.0099 0.0096 0.0094 0.0091 0.0089 0.0087 0.0084 -2.3 0.0107 0.0104 0.0136 0.0132 0.0129 0.0125 0.0122 0.01 19 0.0116 0.0113 0.01 10 -2.2 0.0139 0.0143 -2.1 0.0179 0.0174 0.0170 0.0166 0.0162 0.0158 0.0154 0.0150 0.0146 -2.0 0.0228 0.0222 0.0217 0.0212 0.0207 0.0202 0.0197 0.0192 0.0188 0.0183 0.0287 0.0281 0.0274 0.0268 0.0262 0.0256 0.0250 0.0244 0.0239 0.0233 -1. 0.0322 0.0301 0.0294 0.0359 0.0351 0.0344 0.0336 0.0329 0.0314 0.0307 0.0427 0.0418 0.0409 0.0401 0.0392 0.0384 0.0375 0.0367 0.0446 0.0436 0.0548 0.0537 0.0526 0.0516 0.0505 0.0495 0.0485 0.0475 0.0465 0.0455 -1.6 0.0571 0.0559 -1.5 0.0668 0.0655 0.0643 0.0630 0.0618 0.0606 0.0594 0.0582 0.0681 0.0808 0.0793 0.0778 0.0764 0.0749 0.0735 0.0721 0.0708 0.0694 0.0934 0.0918 0.0901 0.0885 0.0869 0.0853 0.0838 0.0823 0.0968 0.0951 0.1131 0. 1093 0.1003 0.0985 0.1151 0.1112 0.1075 0.1056 0.1038 0.1020 0.1170 1.1 0.1357 0.1335 0.1314 0.1292 0.1271 0.1251 0.1230 0.1210 0.1190 0.1401 0.1379 10 0.1587 0.1562 0.1539 0.1515 0.1492 0.1469 0.1446 0.1423 -0.9 0.1841 0.1814 0.1788 0.1762 0.1736 0.1711 0.1685 0.1660 0.1635 0.1611 -0.8 0.2119 0.2090 0.2061 0.2033 0.2005 0.1977 0.1949 0.1922 0.1894 0.1867 -0.7 0.2389 0.2358 0.2296 0.2266 0.2236 0.2206 0.2177 0.2148 0.2420 0.2327 0.2451 -0.6 0.2743 0.2709 0.2676 0.2643 0.2611 0.2578 0.2546 0.2514 0.2483 -0.5 0.3085 0.3050 0.3015 0.2981 0.2946 0.2912 0.2877 0.2843 0.2810 0.2776 -0.4 0.3446 0.3409 0.3372 0.3336 0.3300 0.3264 0.3228 0.3192 0.3156 0.3121 0.3594 0.3557 0.3520 0.3483 -0.3 0.3821 0.3783 0.3745 0.3707 0.3669 0.3632 0.4207 0.4052 0.3936 0.3859 -0.2 0.4168 0.4129 0.4090 0.4013 0.3974 0.3897 -0.1 0.4602 0.4562 0.4522 0.4483 0.4443 0.4404 0.4364 0.4325 0.4286 0.4247 0.5000 0.4960 0.4920 0.4880 0.4840 0.4801 0.4761 0.4721 0.4681 0.4641 -0.0 0.5000 0.5040 0.5080 0.5120 0.5160 0.5199 0.5239 0.5279 0.5319 0.5359 0.0 0.5438 0.5478 0.5517 0.5557 0.5596 0.5636 0.5675 0.5714 0.5753 0.1 0.5398 0.6026 0.6064 0.6103 0.6141 0.2 0.5793 0.5832 0.5871 0.5910 0.5948 0.5987 0.6179 0.6217 0.6255 0.6293 0.6331 0.6368 0.6406 0.6443 0.6480 0.6517 0.3 0.6879 0.4 0.6591 0.6700 0.6736 0.6844 0.6554 0.6628 0.6664 0.6772 0.6808 0.6985 0.7019 0.7054 0.7088 0.7123 0.7157 0.7190 0.7224 0.5 0.6915 0.6950 0.6 0.7257 0.7291 0.7324 0.7357 0.7389 0.7422 0.7454 0.7486 0.7517 0.7549 0.7 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 0.8485 0.8508 0.8554 0.8599 0.8621 1.0 0.8413 0.8438 0.8461 0.8531 0.8577 0.8810 0.8830 0.8643 0.8665 0.8686 0.8708 0.8729 0.8749 0.8770 0.8790 0.9015 0.8849 0.8869 0.8888 0.8907 0.8925 0.8944 0.8962 0.8980 0.8997 0.9032 0.9049 0.9066 0.9082 0.9099 0.9115 0.9131 0.9147 0.9162 0.9177 0.9192 0.9207 0.9222 0.9236 0.9251 0.9265 0.9279 0.9292 0.9306 0.9319 0.9357 0.9370 0.9382 0.9394 0.9406 0.9418 0.9429 0.9441 0.9332 0.9345 0.9495 0.9505 0.9535 0.9545 0.9452 0.9463 0.9474 0.9484 0.9515 0.9525 0.9554 0.9564 0.9573 0.9582 0.9591 0.9599 0.9608 0.9616 0.9625 0.9633 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 20 0.9778 0.9783 0.9788 0.9793 0.9798 0.9803 0.9808 0.9812 0.9817 0.9772 0.9821 0.9826 0.9830 0.9834 0.9838 0.9842 0.9846 0.9850 0.9854 0.9857 2.1 0.9861 0.9864 0.9868 0.9871 0.9875 0.9878 0.9881 0.9884 0.9887 0.9890 2.2 2.3 0.9893 0.9896 0.9898 0.9901 0.9904 0.9906 0.9909 0.9911 0.9913 0.9916 0.9922 0.9925 0.9927 0.9929 0.9931 0.9932 0.9934 0.9936 2.4 0.9918 0.9920 0.9952 2.5 0.9938 0.9940 0.9941 0.9943 0.9945 0.9946 0.9948 0.9949 0.9951 0.9956 0.9957 0.9959 0.9960 0.9961 0.9962 0.9963 0.9964 2.6 0.9953 0.9955 0.9965 0.9966 0.9967 0.9968 0.9969 0.9970 0.9971 0.9972 0.9973 0.9974 2.7 0.9976 0.9977 0.9977 0.9978 0.9979 0.9979 0.9980 0.9981 2.8 0.9974 0.9975 2.9 0.9981 0.9982 0.9982 0.9983 0.9984 0.9984 0.9985 0.9985 0.9986 0.9986 0.9990 3.0 0.9987 0.9987 0.9987 0.9988 0.9988 0.9989 0.9989 0.9989 0.9990 3.1 0.9990 0.9991 0.9991 0.9991 0.9992 0.9992 0.9992 0.9992 0.9993 0.9993 0.9995 3.2 0.9993 0.9993 0.9994 0.9994 0.9994 0.9994 0.9994 0.9995 0.9995 0.9996 0.9997 3.3 0.9995 0.9995 0.9995 0.9996 0.9996 0.9996 0.9996 0.9996 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9998 3.4 0.9998 0.9998 0.9998 3.5 0.9998 0.9998 0.9998 0.9998 0.9998 0.9998 0.9998 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 3.6 0.9998 0.9998 3.7 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 0.9999 0.9999 0.9999 0.9999 0.9999 3.8 1.0000 39 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 Source: Probabilities calculated with Excel