a. What is the standard deviation of the average fill volume of 100 cans? b. If the mean fill volume is 12.1 oz, what is the probability that the average fill volume of 100 cans is less than 12 oz? c. What should the mean fill volume equal so that the probability that the average of 100 cans is less than 12 oz is 0.005?

a. What is the standard deviation of the average fill volume of 100 cans? b. If the mean fill volume is 12.1 oz, what is the probability that the average fill volume of 100 cans is less than 12 oz? c. What should the mean fill volume equal so that the probability that the average of 100 cans is less than 12 oz is 0.005?

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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Question

5.6.6 WP An automated filling machine fills soft-drink cans,
and the standard deviation is 0.5 fluid ounce. Assume that the fill
volumes of the cans are independent, normal random variables.
a. What is the standard deviation of the average fill volume
of 100 cans?
b. If the mean fill volume is 12.1 oz, what is the probability
that the average fill volume of 100 cans is less than 12 oz?
c. What should the mean fill volume equal so that the
probability that the average of 100 cans is less than 12 oz
is 0.005?
d. If the mean fill volume is 12.1 oz, what should the stan-
dard deviation of fill volume equal so that the probability that
the average of 100 cans is less than 12 oz is 0.005?
e. Determine the number of cans that need to be measured
such that the probability that the average fill volume is less
than 12 oz is 0.01.

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Follow-up Question

Using the information obtained above, complete the following:

d. If the mean fill volume is 12.1 oz, what should the stan-
dard deviation of fill volume equal so that the probability that
the average of 100 cans is less than 12 oz is 0.005?
e. Determine the number of cans that need to be measured
such that the probability that the average fill volume is less
than 12 oz is 0.01.

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