7.2

14. The time required for an automotive center to complete an oil change service on an automobile approximately follows a normal distribution, with a mean of 15 minutes and a standard deviation of 4 minutes. (a) The automotive center guarantees customers that the service will take no longer than 20 minutes. If it does take longer, the customer will receive the service for half-price. What percent of customers receive the service for half-price? (b) If the automotive center does not want to give the discount to more than 7% of its customers, how long should it make the guaranteed time limit? Click here to view the standard normal distribution table (page 1). 34 Click here to view the standard normal distribution table (page 2), 35 (a) The percent of customers that receive the service for half-price is %. Round to two decimal places as needed.) (b) The guaranteed time limit is minutes. Round up to the nearest minute.) 34: Standard Normal Distribution Table (page 1) Standard Normal Distribution Z 0.90 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.0605 97 6 0.0003 0.0003 -3.3 0.0003 0.0005 9.0003 0.0005 0.0005 0.0005 0.0004 0.0004 0.0004 0.0004 0.000 0.0003 -32 0.0007 0.000 0.0006 0.0006 0.0006 0.0006 0.0006 0.0005 0.0005 0.0005 -3.1 0.0010 0.000 0.0009 0.0009 0.0008 0.0008 0.0008 0.0008 0.0007 0.0007 -3.0 0.0013 0.0013 0.0013 0.0012 0.0012 0.0011 0.0011 0.0011 0.0010 0.0010 -29 0.0019 0.0018 0.0018 0.001 0.0016 0.0016 0.0015 0.0015 0.0014 0.0014 0.0026 0.0024 0.0023 0.0023 0.0022 0.0021 0.0021 0.0020 0.0019 -2.7 0.0035 0.003 .0033 0.0032 0.0031 0.0030 0.0029 0.0028 0.0027 0.0026 -2.6 0.0047 0.0044 0.004 0.0041 0.0040 0.0030 0.0038 0.0037 -2.5 0.0062 0.0055 0.0054 0.0032 0.0051 0 0010 0.0036 0.0048 0.0082 0.0078 0.007 0.0073 0.007 0.0060 0.006 0.0066 0.006 -2.3 0.0107 0.0102 0.0099 0.0094 0 0089 -2.2 0.0139 0.013 0.0132 0.012 0.0125 0.0122 0.0119 0.0116 0.0113 0.0110 0.0179 0.0174 0.0170 0.0166 0.0162 0.015 0.0154 0.0150 0.0146 0.0143 -2.0 0.0228 0.0222 0.0217 0.0212 0.0207 0.0202 0.0197 0.0192 0.0188 0.0183 0.028 0.0281 0.027 0.0268 0.0262 0.025 0.0250 0.024 0.0230 0.0233 -1.8 0.0359 0.0351 0.0344 0.033 0.0329 0.0322 0.0314 0.0307 0.0301 0.0204 -1.7 0.0446 0.0436 0.0427 0.0418 0.0409 0.0401 0.0392 0.0384 0.0375 0.0367 -1.6 0.054 0.0537 0.052 0.0516 0.0505 0.049 0.0485 0.0475 0.0465 0.0455 -1.5 0.0668 0.0655 0.0643 0.0630 0.0618 0.060 0.0594 0.0582 0.0571 0.0559 0.080 0.0793 0.077 0.076 0.0749 0.073 0.0721 0.0708 0.069 0.068 -13 0.0968 0.095 0.0934 0.0918 0.0901 0.088 0.0860 0.0853 0.0838 0.0823 -1.2 0.1151 0.1131 012 0.109 -1.1 0.1075 0.105 0.1038 0.1020 0.0985 0.1357 0.1335 0.1314 0.1292 0.1271 0.1251 0.1230 0.1210 0.1190 0.1170 -1.0 0.1587 0.1562 0.1539 0.1515 0.1492 0.1469 0.1446 0.1423 0.1401 0.1379 .1841 0.1814 0.178 0.176 0.1736 0.1711 0.1685 0.1660 .1635 0.2119 0.2096 0.2061 0.2033 0.2005 0.1977 0.1949 0.192 0.189 0.1867 0.2420 0.2389 0.2358 0:2327 0.2296 0.2266 0.2236 0.2206 0.2177 0.2148 0.2743 0.2709 0.2676 0.264 0.2611 0.2578 0.2546 0.2514 0.2483 0.2451 0.3085 0.305 0.3015 0.298 0.2946 0.2877 0.2843 0.2810 0.2776 0.3446 0.3409 0.3372 0.333 0.3300 0.3264 0.3228 0.3192 0.3156 0.3121 0.3821 0.378 0.3745 0.370 0.3669 0.3632 0.3594 0.355 0.3520 0.348 -0.2 0.4207 0.4168 0.4129 0.4090 0.4052 0.4013 0.3974 0.393 0.3897 0.3859 0.4602 0.4562 0.4522 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 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 35: Standard Normal Distribution Table (page 2) A Standard Normal Distribution z 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.0 0.5000 0.5040 0.5080 0.5120 0.5160 0.5199 0.5239 0.5478 0.5279 0.531 0.5359 0.1 0.5398 0.5438 0.5517 0.5636 0.5675 0.5714 0.5753 0.2 0.5793 0 58 32 02671 0.5910 0.6026 0.6103 0.6141 03 0.6179 0.6217 0.6255 0.6293 0.6331 0.640 0.6443 0.648 0.6517 0.4 0.6554 0.6591 0.6628 0.6664 0.6700 0.6772 0.6808 0.6844 0.6879 1.5 0.6915 0.6950 0.6985 0.7019 0.7054 0.7123 0.7157 0.710 0.7224 0.6 0.7257 0.7201 0.7324 0.7357 0.7380 0.7422 0.7454 0.7486 0.7517 0.7540 07 0.7560 0.7611 0.7612 0.7673 0.7704 0.7734 0.1764 0.7794 0.7823 0.8 0.7881 0.7010 0.7939 0.7967 0.799 0.8023 0.805 0.8078 0.810 0.813 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 0.846 0.8485 0.8508 0.8531 0.855 .8577 0.8599 0.8621 1.1 0.8643 0.8665 0.8686 0.8708 0.8729 0.8749 0.8770 0.8790 0.8830 1.2 0.8849 0.8869 0.8888 0.8907 0.8925 0.8944 0.8962 0.8980 0.8997 0.9015 13 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 0.9332 0.9345 0.9357 0.9370 0.9382 0.9394 0.9406 0.9418 0.9429 0.9441 0.9452 0.9463 0.9474 0.918 0.9495 0.9505 0.951 0.9525 0.9535 0.9545 1.7 0.9554 0.9564 0.9573 0.9582 0.9591 0.9599 0.960 0.9616 0.9625 0.9633 0.9641 0.9649 0.9664 0.9671 0.9678 0.968 0.9699 0.9706 0.9713 0.9719 0.972 0.9732 0.9738 0.9744 0.9750 0.9756 0.976 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 0.98 0.9826 0.9830 0.983 0.9838 0.9842 3.984 0.9850 0.9854 0.9857 2.2 0.9861 0.9864 0.9868 0.9871 0.9875 0.9878 0.988 0.9884 0.9887 0.9890 2.3 09003 0.9896 0.9898 0.9901 0.9904 0.9906 0.9909 0.901 1 0.9913 0.9916 2.4 0.9918 0.9920 0.9927 0.9925 0.9927 0.9929 0.9931 0.9932 0.993 0.993 2.5 0.9938 0.9940 0.9041 0.994 0.9946 0.994 0.995 0.9952 26 0.9953 0.9955 0.995 0.9957 0.995 0.9960 0.996 0.9962 0.996 0.9964 27 0.9965 0.9966 0.9967 0.9968 0.9969 0.9970 0.9971 0.9972 0.9973 0.9974 0.9974 0.9975 0.9976 0.9977 0.9977 0.9978 0.9979 0.9979 0.9980 0.9981 0.9981 0.9082 0.998 0.9083 0.9984 0.9084 0.9985 0.9985 0.9986 0.9986 0.9987 0.908 0.9988 0.998 0.9989 0.998 0.9989 0.999 0.9990 0.9990 0.9991 0.909 0.9991 0.999 0.9992 0.999 0.9992 0.9993 32 0.9993 0.9993 0.9993 0.9994 0.9994 0.9994 0.999 0.9995 0.9995 0.9995 3.3 0.9995 0.9095 0.9995 0.9996 0.9996 0.9996 0.999 0.9996 0.9996 0.9997 0.9997 0.9997 0.9097 0.9997 0.9997 0.9097 0.9997 0.9997 0.9997 0.9998 Z 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 7.2