The heights of North American women are normally distributed with a mean of 64 inches and a standard deviation of 2 inches. a) What is the probability that a randomly selected woman is taller than 66 inches? b) A random sample of four women is selected. What is the probability that the sample mean height is greater than 66 inches? c) What is the probability that the mean height of a random sample of 100 women is greater than 66 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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The heights of North American women are normally distributed with a mean of 64 inches and a standard deviation of 2 inches.

a) What is the probability that a randomly selected woman is taller than 66 inches?

b) A random sample of four women is selected. What is the probability that the sample mean height is greater than 66 inches?

c) What is the probability that the mean height of a random sample of 100 women is greater than 66 inches?

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