A manufacturer knows that their items have a normally distributed length, with a mean of 10 inches, and standard deviation of 3.2 inches. If 3 items are chosen at random, what is the probability that their mean length is less than 12.2 inches?

College Algebra
10th Edition
ISBN:9781337282291
Author:Ron Larson
Publisher:Ron Larson
Chapter8: Sequences, Series,and Probability
Section8.7: Probability
Problem 11ECP: A manufacturer has determined that a machine averages one faulty unit for every 500 it produces....
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A manufacturer knows that their items have a normally distributed length, with a mean of 10 inches, and standard deviation of 3.2 inches.

If 3 items are chosen at random, what is the probability that their mean length is less than 12.2 inches?

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