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A soft-drink machine at a steak house is regulated so that the amount of drink dispensed is approximately normally distributed with a mean of 210 milliliters and a standard deviation of 8 milliliters. The machine is checked periodically by sample of 16 drinks and computing the average content. If x falls in the interval 203

A soft-drink machine at a steak house is regulated so that the amount of drink dispensed is approximately normally distributed with a mean of 210 milliliters and a standard deviation of 8 milliliters. The machine is checked periodically by sample of 16 drinks and computing the average content. If x falls in the interval 203

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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. Arcas under the Normal Curve .00 .01 .02 .03 .04 .05 .06 .07 .08 .09 0.0 0.5040 0.5120 0.5160 0.5557 0.5948 0.5000 0.5080 0.5199 0.5239 0.5279 0.5319 0.5359 0.0 0.1 0,5714 0.6103 0,5753 0.6141 0.5398 0.5438 0.5478 0.5517 0.5596 0.5636 0.5675 0.1 0.5793 0.6026 0.6406 0.6772 0.2 0.6064 0.5832 0.6217 0.5871 0.5910 0.5987 0.2 0.6255 0.6628 0.6293 0.6664 0.6179 0.6331 0.6368 0.6443 0.6808 0.6480 0.6517 0.3 0.4 0.3 0.4 0.6554 0.6591 0.6700 0.6736 0.6844 0.6879 0.5 0.6950 0.7291 0.7611 0.7054 0.7389 0.7704 0.7088 0.7422 0.7734 0.7190 0.7517 0.7823 0.6915 0.6985 0.7019 0.7123 0.7157 0.7224 0.5 0.6 0.7257 0.7324 0.7642 0.7357 0.7454 0.7486 0.7549 0.7852 0.6 0.7 0.7580 0.7673 0.7764 0.7794 0.7 0.7967 0.8238 0.7995 0.8264 0.8023 0.8289 0.8051 0.8 0.9 0.7881 0.8159 0.8078 0.8340 0.7910 0.7939 0.8106 0.8133 0.8 0.8186 0.8212 0.8315 0.8365 0.8389 0.9 0.8508 0.8729 0.8925 0.9099 1.0 0.8413 0.8438 0.8461 0.8485 0.8531 0.8554 0.8577 0.8599 0.8621 1.0 1.1 0.8643 0.8665 0.8686 0.8708 0.8749 0.8770 0.8790 0.8810 0.8830 1.1 0.8944 0.9115 0.8962 0.8980 0.9147 1.2 1.2 1.3 0.8849 0.8869 0.8888 0.8907 0.8997 0.9015 0.9032 0.9049 0.9066 0.9082 0.9131 0.9162 0.9177 1.3 1.4 0.9192 0.9207 0.9222 0.9236 0.9251 0.9265 0.9279 0.9292 0.9306 0.9319 1.4 1.5 0,9332 0.9345 0.9357 0.9370 0.9382 0.9394 0.9406 0.9418 0.9429 0.9441 1.5 1.6 0.9452 0.9463 0.9474 0.9484 0.9582 0.9664 0.9495 0.9505 0.9515 0.9608 0.9525 0.9616 0.9693 0.9535 0.9545 1.6 1.7 0.9554 0.9564 0.9573 0.9591 0.9599 0.9625 0.9633 1.7 1.8 0.9641 0.9649 0.9656 0.9671 0.9678 0.9686 0.9699 0.9706 1.8 1.9 0.9713 0.9719 0.9726 0.9732 0.9738 0.9744 0.9750 0.9756 0.9761 0.9767 1.9 2.0 0,9772 0.9778 0,9783 0,9788 0,9793 0.9798 0.9803 0.9808 0.9812 0,9817 2.0 2.1 2.2 2.3 2.4 0.9821 0.9861 0.9826 0.9830 0.9834 0.9838 0.9875 0.9904 0.9842 0.9846 0.9850 0.9884 0.9911 0.9932 0.9854 0.9887 0.9913 0.9934 0.9857 0.9890 0.9916 0.9936 2.1 2.2 2.3 2.4 0.9864 0.9868 0.9871 0.9878 0.9881 0.9896 0.9898 0.9901 0.9925 0.9893 0.9909 0.9906 0.9929 0.9918 0.9920 0.9922 0.9927 0.9931 2.5 0.9938 0.9940 0.9941 0.9943 0.9945 0.9946 0.9948 0.9949 0.9951 0.9952 2.5 0.9953 0.9965 0.9960 0.9970 0.9978 0.9961 0.9971 0.9979 0.9985 0.9962 0.9972 0.9979 0.9963 0.9973 0.9980 2.6 0.9955 0.9956 0.9957 0.9959 0.9964 0.9974 2.6 2.7 2.8 2.7 0.9966 0.9967 0.9968 0.9969 2.8 2.9 0.9974 0.9975 0.9976 0.9982 0.9982 0.9983 0.9977 0.9977 0.9981 0.9981 0.9984 0.9984 0.9985 0.9986 0.9986 2.9 Print Done
Transcribed Image Text:. Arcas under the Normal Curve .00 .01 .02 .03 .04 .05 .06 .07 .08 .09 0.0 0.5040 0.5120 0.5160 0.5557 0.5948 0.5000 0.5080 0.5199 0.5239 0.5279 0.5319 0.5359 0.0 0.1 0,5714 0.6103 0,5753 0.6141 0.5398 0.5438 0.5478 0.5517 0.5596 0.5636 0.5675 0.1 0.5793 0.6026 0.6406 0.6772 0.2 0.6064 0.5832 0.6217 0.5871 0.5910 0.5987 0.2 0.6255 0.6628 0.6293 0.6664 0.6179 0.6331 0.6368 0.6443 0.6808 0.6480 0.6517 0.3 0.4 0.3 0.4 0.6554 0.6591 0.6700 0.6736 0.6844 0.6879 0.5 0.6950 0.7291 0.7611 0.7054 0.7389 0.7704 0.7088 0.7422 0.7734 0.7190 0.7517 0.7823 0.6915 0.6985 0.7019 0.7123 0.7157 0.7224 0.5 0.6 0.7257 0.7324 0.7642 0.7357 0.7454 0.7486 0.7549 0.7852 0.6 0.7 0.7580 0.7673 0.7764 0.7794 0.7 0.7967 0.8238 0.7995 0.8264 0.8023 0.8289 0.8051 0.8 0.9 0.7881 0.8159 0.8078 0.8340 0.7910 0.7939 0.8106 0.8133 0.8 0.8186 0.8212 0.8315 0.8365 0.8389 0.9 0.8508 0.8729 0.8925 0.9099 1.0 0.8413 0.8438 0.8461 0.8485 0.8531 0.8554 0.8577 0.8599 0.8621 1.0 1.1 0.8643 0.8665 0.8686 0.8708 0.8749 0.8770 0.8790 0.8810 0.8830 1.1 0.8944 0.9115 0.8962 0.8980 0.9147 1.2 1.2 1.3 0.8849 0.8869 0.8888 0.8907 0.8997 0.9015 0.9032 0.9049 0.9066 0.9082 0.9131 0.9162 0.9177 1.3 1.4 0.9192 0.9207 0.9222 0.9236 0.9251 0.9265 0.9279 0.9292 0.9306 0.9319 1.4 1.5 0,9332 0.9345 0.9357 0.9370 0.9382 0.9394 0.9406 0.9418 0.9429 0.9441 1.5 1.6 0.9452 0.9463 0.9474 0.9484 0.9582 0.9664 0.9495 0.9505 0.9515 0.9608 0.9525 0.9616 0.9693 0.9535 0.9545 1.6 1.7 0.9554 0.9564 0.9573 0.9591 0.9599 0.9625 0.9633 1.7 1.8 0.9641 0.9649 0.9656 0.9671 0.9678 0.9686 0.9699 0.9706 1.8 1.9 0.9713 0.9719 0.9726 0.9732 0.9738 0.9744 0.9750 0.9756 0.9761 0.9767 1.9 2.0 0,9772 0.9778 0,9783 0,9788 0,9793 0.9798 0.9803 0.9808 0.9812 0,9817 2.0 2.1 2.2 2.3 2.4 0.9821 0.9861 0.9826 0.9830 0.9834 0.9838 0.9875 0.9904 0.9842 0.9846 0.9850 0.9884 0.9911 0.9932 0.9854 0.9887 0.9913 0.9934 0.9857 0.9890 0.9916 0.9936 2.1 2.2 2.3 2.4 0.9864 0.9868 0.9871 0.9878 0.9881 0.9896 0.9898 0.9901 0.9925 0.9893 0.9909 0.9906 0.9929 0.9918 0.9920 0.9922 0.9927 0.9931 2.5 0.9938 0.9940 0.9941 0.9943 0.9945 0.9946 0.9948 0.9949 0.9951 0.9952 2.5 0.9953 0.9965 0.9960 0.9970 0.9978 0.9961 0.9971 0.9979 0.9985 0.9962 0.9972 0.9979 0.9963 0.9973 0.9980 2.6 0.9955 0.9956 0.9957 0.9959 0.9964 0.9974 2.6 2.7 2.8 2.7 0.9966 0.9967 0.9968 0.9969 2.8 2.9 0.9974 0.9975 0.9976 0.9982 0.9982 0.9983 0.9977 0.9977 0.9981 0.9981 0.9984 0.9984 0.9985 0.9986 0.9986 2.9 Print Done
A soft-drink machine at a steak house is regulated so that the amount of drink dispensed is approximately normally distributed with a mean of 210 milliliters and a standard deviation of 8 milliliters. The machine is checked periodically by taking a sample of 16 drinks and computing the average content. If x falls in the interval 203 <x<217, the machine is thought to be operating satisfactorily; otherwise, the owner concludes that u +210 milliliters. Complete parts (a) and (b) below. Click here to view page 1 of the standard normal distribution table. Click here to view page 2 of the standard normal distribution table. (a) Find the probability of committing a type I error when u =210 milliliters. The probability is .0004 . (Round to four decimal places as needed.) (b) Find the probability of committing a type Il error when u = 202 milliliters. The probability is: (Round to four decimal places as needed.)
Transcribed Image Text:A soft-drink machine at a steak house is regulated so that the amount of drink dispensed is approximately normally distributed with a mean of 210 milliliters and a standard deviation of 8 milliliters. The machine is checked periodically by taking a sample of 16 drinks and computing the average content. If x falls in the interval 203 <x<217, the machine is thought to be operating satisfactorily; otherwise, the owner concludes that u +210 milliliters. Complete parts (a) and (b) below. Click here to view page 1 of the standard normal distribution table. Click here to view page 2 of the standard normal distribution table. (a) Find the probability of committing a type I error when u =210 milliliters. The probability is .0004 . (Round to four decimal places as needed.) (b) Find the probability of committing a type Il error when u = 202 milliliters. The probability is: (Round to four decimal places as needed.)
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