Homework Help is Here – Start Your Trial Now!
Math
Statistics
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 19 minutes and a standard deviation of 2.5 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 4​% of its​ customers, how long should it make the guaranteed time​ limit?

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 19 minutes and a standard deviation of 2.5 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 4​% of its​ customers, how long should it make the guaranteed time​ limit?

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
See similar textbooks
icon
Related questions
Question
100%
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 19 minutes and a standard deviation of 2.5 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 4​% of its​ customers, how long should it make the guaranteed time​ limit?
 
Click here to view the standard normal distribution table (page 1).
Click here to view the standard normal distribution table (page 2).
7/8/22, 2:37 PM ८ 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3.0 3.1 3.2 3.3 3.4 N Area 0.00 0.5000 0.5398 0.5438 0.5793 0.5832 0.6179 0.6554 0.6915 0.7257 0.7580 0.7881 0.8159 0.8413 0.8643 0.8849 0.9032 0.9192 0.9641 0.9713 0.9772 0.9821 0.9861 0.9893 0.9918 0.9938 0.9953 0.9965 0.9974 0.9981 0.9987 0.9990 0.9993 0.01 0.02 0.5040 0.5080 0.5120 0.5160 0.5517 0.5557 0.5478 0.5871 0.5910 0.5948 0.6217 0.6255 0.6293 0.6331 0.6591 0.9995 0.9997 0.00 0.9332 0.9345 0.9357 0.9452 0.9463 0.9474 0.9554 0.9564 0.9573 0.6950 0.7019 0.6985 0.7054 0.7291 0.7324 0.7357 0.7389 0.7611 0.7642 0.7673 0.7704 0.7910 0.7939 0.8186 0.8212 0.8438 0.8461 0.8665 0.8869 0.9049 0.9207 0.6628 0.6664 0.6700 0.6736 0.9940 0.9955 0.9966 0.9975 0.9982 0.9066 0.9222 Standard Normal Distribution 0.03 0.04 0.05 0.8485 0.8686 0.8708 0.8888 0.8907 0.9995 0.9997 0.01 0.7967 0.8238 0.9370 0.9382 0.9484 0.9495 0.9582 0.9591 0.9649 0.9656 0.9664 0.9671 0.9719 0.9726 0.9732 0.9738 0.9987 0.9987 0.9991 0.9991 0.9993 0.9994 0.9082 0.9236 0.9778 0.9783 0.9788 0.9793 0.9826 0.9830 0.9834 0.9838 0.9864 0.9868 0.9871 0.9875 0.9896 0.9898 0.9901 0.9904 0.9920 0.9922 0.9925 0.9927 0.9941 0.9943 0.9956 0.9957 0.9967 0.9968 0.9995 0.9997 0.02 0.9976 0.9977 0.9982 0.9983 0.7088 0.7422 0.7734 0.7995 0.8023 0.8264 0.8289 0.9996 0.9997 0.03 Standard Normal Distribution Table (page 2) 0.9945 0.9959 0.8508 0.8531 0.8729 0.8749 0.8770 0.8925 0.8944 0.8962 0.9099 0.9115 0.9251 0.9265 0.9969 0.9977 0.9984 0.9988 0.9988 0.9991 0.9992 0.9994 0.9994 0.06 0.07 0.5199 0.5239 0.5279 0.5596 0.5636 0.5675 0.5987 0.6026 0.6064 0.6368 0.6406 0.6443 0.6480 0.6772 0.6808 0.6844 0.9996 0.9997 0.04 0.7123 0.7454 0.7764 0.9946 0.9960 0.9970 0.9978 0.9984 0.9989 0.9992 0.9994 0.9996 0.9997 0.05 0.7157 0.7190 0.7486 0.7517 0.7794 0.7823 0.8051 0.8106 0.8078 0.8315 0.8340 0.8365 0.8554 0.8577 0.8790 0.8980 0.9394 0.9406 0.9418 0.9505 0.9515 0.9525 0.9599 0.9608 0.9616 0.9678 0.9686 0.9744 0.9750 0.9803 0.9842 0.9846 0.9878 0.9881 0.9906 0.9909 0.9798 0.9929 0.9931 0.9131 0.9147 0.9279 0.9292 0.9948 0.9961 0.9971 0.9979 0.9985 0.08 0.5319 0.5714 0.6103 0.9996 0.9997 0.06 0.8599 0.8810 0.8997 0.9162 0.9306 0.9693 0.9699 0.9756 0.9761 0.9808 0.9812 0.9850 0.9854 0.9884 0.9887 0.9911 0.9913 0.9932 0.9934 0.9996 0.9997 0.07 0.9949 0.9951 0.9962 0.9963 0.9972 0.9973 0.9979 0.9980 0.9985 0.9986 0.9989 0.9989 0.9990 0.9992 0.9992 0.9993 0.9994 0.9995 0.9995 0.9429 0.9441 0.9535 0.9545 0.9625 0.9633 0.09 0.5359 0.5753 0.6141 0.9996 0.9997 0.08 0.6517 0.6879 0.7224 0.7549 0.7852 0.8133 0.8389 0.8621 0.8830 0.90 15 0.9177 0.9319 0.9706 0.9767 0.9817 0.9857 0.9890 0.9916 0.9936 0.9952 0.9964 0.9974 0.9981 0.9986 0.9990 0.9993 0.9995 0.9997 0.9998 0.09
Transcribed Image Text:7/8/22, 2:37 PM ८ 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3.0 3.1 3.2 3.3 3.4 N Area 0.00 0.5000 0.5398 0.5438 0.5793 0.5832 0.6179 0.6554 0.6915 0.7257 0.7580 0.7881 0.8159 0.8413 0.8643 0.8849 0.9032 0.9192 0.9641 0.9713 0.9772 0.9821 0.9861 0.9893 0.9918 0.9938 0.9953 0.9965 0.9974 0.9981 0.9987 0.9990 0.9993 0.01 0.02 0.5040 0.5080 0.5120 0.5160 0.5517 0.5557 0.5478 0.5871 0.5910 0.5948 0.6217 0.6255 0.6293 0.6331 0.6591 0.9995 0.9997 0.00 0.9332 0.9345 0.9357 0.9452 0.9463 0.9474 0.9554 0.9564 0.9573 0.6950 0.7019 0.6985 0.7054 0.7291 0.7324 0.7357 0.7389 0.7611 0.7642 0.7673 0.7704 0.7910 0.7939 0.8186 0.8212 0.8438 0.8461 0.8665 0.8869 0.9049 0.9207 0.6628 0.6664 0.6700 0.6736 0.9940 0.9955 0.9966 0.9975 0.9982 0.9066 0.9222 Standard Normal Distribution 0.03 0.04 0.05 0.8485 0.8686 0.8708 0.8888 0.8907 0.9995 0.9997 0.01 0.7967 0.8238 0.9370 0.9382 0.9484 0.9495 0.9582 0.9591 0.9649 0.9656 0.9664 0.9671 0.9719 0.9726 0.9732 0.9738 0.9987 0.9987 0.9991 0.9991 0.9993 0.9994 0.9082 0.9236 0.9778 0.9783 0.9788 0.9793 0.9826 0.9830 0.9834 0.9838 0.9864 0.9868 0.9871 0.9875 0.9896 0.9898 0.9901 0.9904 0.9920 0.9922 0.9925 0.9927 0.9941 0.9943 0.9956 0.9957 0.9967 0.9968 0.9995 0.9997 0.02 0.9976 0.9977 0.9982 0.9983 0.7088 0.7422 0.7734 0.7995 0.8023 0.8264 0.8289 0.9996 0.9997 0.03 Standard Normal Distribution Table (page 2) 0.9945 0.9959 0.8508 0.8531 0.8729 0.8749 0.8770 0.8925 0.8944 0.8962 0.9099 0.9115 0.9251 0.9265 0.9969 0.9977 0.9984 0.9988 0.9988 0.9991 0.9992 0.9994 0.9994 0.06 0.07 0.5199 0.5239 0.5279 0.5596 0.5636 0.5675 0.5987 0.6026 0.6064 0.6368 0.6406 0.6443 0.6480 0.6772 0.6808 0.6844 0.9996 0.9997 0.04 0.7123 0.7454 0.7764 0.9946 0.9960 0.9970 0.9978 0.9984 0.9989 0.9992 0.9994 0.9996 0.9997 0.05 0.7157 0.7190 0.7486 0.7517 0.7794 0.7823 0.8051 0.8106 0.8078 0.8315 0.8340 0.8365 0.8554 0.8577 0.8790 0.8980 0.9394 0.9406 0.9418 0.9505 0.9515 0.9525 0.9599 0.9608 0.9616 0.9678 0.9686 0.9744 0.9750 0.9803 0.9842 0.9846 0.9878 0.9881 0.9906 0.9909 0.9798 0.9929 0.9931 0.9131 0.9147 0.9279 0.9292 0.9948 0.9961 0.9971 0.9979 0.9985 0.08 0.5319 0.5714 0.6103 0.9996 0.9997 0.06 0.8599 0.8810 0.8997 0.9162 0.9306 0.9693 0.9699 0.9756 0.9761 0.9808 0.9812 0.9850 0.9854 0.9884 0.9887 0.9911 0.9913 0.9932 0.9934 0.9996 0.9997 0.07 0.9949 0.9951 0.9962 0.9963 0.9972 0.9973 0.9979 0.9980 0.9985 0.9986 0.9989 0.9989 0.9990 0.9992 0.9992 0.9993 0.9994 0.9995 0.9995 0.9429 0.9441 0.9535 0.9545 0.9625 0.9633 0.09 0.5359 0.5753 0.6141 0.9996 0.9997 0.08 0.6517 0.6879 0.7224 0.7549 0.7852 0.8133 0.8389 0.8621 0.8830 0.90 15 0.9177 0.9319 0.9706 0.9767 0.9817 0.9857 0.9890 0.9916 0.9936 0.9952 0.9964 0.9974 0.9981 0.9986 0.9990 0.9993 0.9995 0.9997 0.9998 0.09
7/8/22, 2:37 PM Area N -3.4 -3.3 -3.2 -3.1 -3.0 -29 -2.8 -2.7 -2.6 -2.5 -2.4 -2.3 -2.2 -2.1 -2.0 -1.9 -1.8 -1.7 -1.6 -1.5 -1.0 -0.9 -0.8 -0.7 -0.6 -0.5 -0.4 -0.3 -0.2 -0.1 -0.0 N 0.00 0.0003 0.0005 0.0007 0.0010 0.0013 0.01 0.0003 0.0005 0.0007 0.0009 0.0013 0.0019 0.0018 0.0026 0.0025 0.0035 0.0034 0.0033 0.0047 0.0062 0.02 0.0003 0.0005 0.0006 0.0179 0.0174 0.0228 0.0222 0.0009 0.0013 0.0082 0.0080 0.0078 0.0107 0.0104 0.0102 0.0139 0.0136 0.0132 0.00 0.2743 0.2709 0.3085 0.3050 0.0170 0.0217 Standard Normal Distribution 0.03 0.04 0.05 0.0003 0.0004 0.0006 0.0018 0.0017 0.0024 0.0023 0.0023 0.0032 0.0031 0.0045 0.0044 0.0043 0.0041 0.0055 0.0060 0.0059 0.0057 0.0003 0.0004 0.0006 0.0009 0.0008 0.0012 0.0166 0.0212 0.0075 0.0099 0.0096 0.0129 0.0125 Standard Normal Distribution Table (page 1) 0.0012 0.0016 0.0016 0.0015 0.0022 0.0030 0.0162 0.0207 0.06 0.0003 0.0003 0.0004 0.0004 0.0006 0.0006 0.0054 0.0052 0.0073 0.0071 0.0069 0.2327 0.2676 0.2643 0.3821 0.3015 0.2981 0.3446 0.3409 0.3372 0.3336 0.3300 0.3783 0.3745 0.3707 0.3669 0.4168 0.4129 0.4090 0.4052 0.4522 0.4483 0.4443 0.4207 0.4602 0.4562 0.5000 0.4960 0.4920 0.4880 0.4840 0.01 0.02 0.03 0.04 0.0008 0.0008 0.0008 0.0011 0.0011 0.0011 0.0015 0.0021 0.0021 0.0029 0.0028 0.0040 0.0039 0.0038 0.0287 0.0281 0.0274 0.0268 0.0262 0.0359 0.0351 0.0344 0.0336 0.0329 0.0668 0.0446 0.0436 0.0427 0.0418 0.0409 0.0548 0.0537 0.0526 0.0516 0.0655 0.0643 0.0630 0.0618 0.0808 0.0793 0.0778 0.0764 0.0749 0.0968 0.0951 0.0934 0.0918 0.0901 0.1151 0.1131 0.1112 0.1093 0.1357 0.1335 0.1314 0.1292 0.1271 0.1492 0.1587 0.1562 0.1814 0.1539 0.1515 0.1788 0.1762 0.1736 0.1841 0.1711 0.1685 0.2119 0.2090 0.2061 0.2033 0.2005 0.1977 0.1949 0.2420 0.2389 0.2358 0.2296 0.2266 0.2236 0.2611 0.2578 0.2546 0.2514 0.2946 0.2912 0.2877 0.0256 0.0322 0.0401 0.0505 0.0495 0.0606 0.0250 0.0314 0.0392 0.07 0.08 0.09 0.0003 0.0003 0.0002 0.0004 0.0004 0.0003 0.0005 0.0005 0.0005 0.0485 0.0594 0.0735 0.0721 0.0885 0.0869 0.1075 0.1056 0.1038 0.0068 0.0089 0.0094 0.0091 0.0122 0.0119 0.0116 0.0158 0.0150 0.0146 0.0154 0.0202 0.0197 0.0192 0.0188 0.1251 0.1230 0.1469 0.1446 0.0007 0.0010 0.0037 0.0051 0.0049 0.0014 0.0020 0.0027 0.0244 0.0307 0.0384 0.0475 0.0582 0.0066 0.0087 0.0113 0.0239 0.0301 0.0375 0.0465 0.0571 0.0708 0.0694 0.0853 0.0838 0.1020 0.1003 0.1210 0.1190 0.1423 0.1401 0.1660 0.1635 0.1922 0.1894 0.2206 0.2177 0.2483 0.2843 0.2810 0.3192 0.3156 0.3264 0.3228 0.3632 0.3594 0.3557 0.3520 0.4013 0.3974 0.3936 0.3897 0.4404 0.4364 0.4325 0.4801 0.4761 0.4721 0.05 0.06 0.07 0.4286 0.4681 0.08 0.0007 0.0010 0.0014 0.0019 0.0026 0.0036 0.0048 0.0064 0.0084 0.0110 0.0143 0.0183 0.0233 0.0294 0.0367 0.0455 0.0559 0.0681 0.0823 0.0985 0.1170 0.1379 0.1611 0.1867 0.2148 0.2451 0.2776 0.3121 0.3483 0.3859 0.4247 0.4641 0.09
Transcribed Image Text:7/8/22, 2:37 PM Area N -3.4 -3.3 -3.2 -3.1 -3.0 -29 -2.8 -2.7 -2.6 -2.5 -2.4 -2.3 -2.2 -2.1 -2.0 -1.9 -1.8 -1.7 -1.6 -1.5 -1.0 -0.9 -0.8 -0.7 -0.6 -0.5 -0.4 -0.3 -0.2 -0.1 -0.0 N 0.00 0.0003 0.0005 0.0007 0.0010 0.0013 0.01 0.0003 0.0005 0.0007 0.0009 0.0013 0.0019 0.0018 0.0026 0.0025 0.0035 0.0034 0.0033 0.0047 0.0062 0.02 0.0003 0.0005 0.0006 0.0179 0.0174 0.0228 0.0222 0.0009 0.0013 0.0082 0.0080 0.0078 0.0107 0.0104 0.0102 0.0139 0.0136 0.0132 0.00 0.2743 0.2709 0.3085 0.3050 0.0170 0.0217 Standard Normal Distribution 0.03 0.04 0.05 0.0003 0.0004 0.0006 0.0018 0.0017 0.0024 0.0023 0.0023 0.0032 0.0031 0.0045 0.0044 0.0043 0.0041 0.0055 0.0060 0.0059 0.0057 0.0003 0.0004 0.0006 0.0009 0.0008 0.0012 0.0166 0.0212 0.0075 0.0099 0.0096 0.0129 0.0125 Standard Normal Distribution Table (page 1) 0.0012 0.0016 0.0016 0.0015 0.0022 0.0030 0.0162 0.0207 0.06 0.0003 0.0003 0.0004 0.0004 0.0006 0.0006 0.0054 0.0052 0.0073 0.0071 0.0069 0.2327 0.2676 0.2643 0.3821 0.3015 0.2981 0.3446 0.3409 0.3372 0.3336 0.3300 0.3783 0.3745 0.3707 0.3669 0.4168 0.4129 0.4090 0.4052 0.4522 0.4483 0.4443 0.4207 0.4602 0.4562 0.5000 0.4960 0.4920 0.4880 0.4840 0.01 0.02 0.03 0.04 0.0008 0.0008 0.0008 0.0011 0.0011 0.0011 0.0015 0.0021 0.0021 0.0029 0.0028 0.0040 0.0039 0.0038 0.0287 0.0281 0.0274 0.0268 0.0262 0.0359 0.0351 0.0344 0.0336 0.0329 0.0668 0.0446 0.0436 0.0427 0.0418 0.0409 0.0548 0.0537 0.0526 0.0516 0.0655 0.0643 0.0630 0.0618 0.0808 0.0793 0.0778 0.0764 0.0749 0.0968 0.0951 0.0934 0.0918 0.0901 0.1151 0.1131 0.1112 0.1093 0.1357 0.1335 0.1314 0.1292 0.1271 0.1492 0.1587 0.1562 0.1814 0.1539 0.1515 0.1788 0.1762 0.1736 0.1841 0.1711 0.1685 0.2119 0.2090 0.2061 0.2033 0.2005 0.1977 0.1949 0.2420 0.2389 0.2358 0.2296 0.2266 0.2236 0.2611 0.2578 0.2546 0.2514 0.2946 0.2912 0.2877 0.0256 0.0322 0.0401 0.0505 0.0495 0.0606 0.0250 0.0314 0.0392 0.07 0.08 0.09 0.0003 0.0003 0.0002 0.0004 0.0004 0.0003 0.0005 0.0005 0.0005 0.0485 0.0594 0.0735 0.0721 0.0885 0.0869 0.1075 0.1056 0.1038 0.0068 0.0089 0.0094 0.0091 0.0122 0.0119 0.0116 0.0158 0.0150 0.0146 0.0154 0.0202 0.0197 0.0192 0.0188 0.1251 0.1230 0.1469 0.1446 0.0007 0.0010 0.0037 0.0051 0.0049 0.0014 0.0020 0.0027 0.0244 0.0307 0.0384 0.0475 0.0582 0.0066 0.0087 0.0113 0.0239 0.0301 0.0375 0.0465 0.0571 0.0708 0.0694 0.0853 0.0838 0.1020 0.1003 0.1210 0.1190 0.1423 0.1401 0.1660 0.1635 0.1922 0.1894 0.2206 0.2177 0.2483 0.2843 0.2810 0.3192 0.3156 0.3264 0.3228 0.3632 0.3594 0.3557 0.3520 0.4013 0.3974 0.3936 0.3897 0.4404 0.4364 0.4325 0.4801 0.4761 0.4721 0.05 0.06 0.07 0.4286 0.4681 0.08 0.0007 0.0010 0.0014 0.0019 0.0026 0.0036 0.0048 0.0064 0.0084 0.0110 0.0143 0.0183 0.0233 0.0294 0.0367 0.0455 0.0559 0.0681 0.0823 0.0985 0.1170 0.1379 0.1611 0.1867 0.2148 0.2451 0.2776 0.3121 0.3483 0.3859 0.4247 0.4641 0.09
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 2 steps with 1 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Similar questions
  • SEE MORE QUESTIONS
Recommended textbooks for you
MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman
Introduction to the Practice of Statistics
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman
SEE MORE TEXTBOOKS