Question

In: Statistics and Probability

A​ half-century ago, the mean height of women in a particular country in their 20s was...

A​ half-century ago, the mean height of women in a particular country in their 20s was 64.7 inches. Assume that the heights of​ today's women in their 20s are approximately normally distributed with a standard deviation of 1.72 inches. If the mean height today is the same as that of a​ half-century ago, what percentage of all samples of 22 of​ today's women in their 20s have mean heights of at least 65.74 ​inches?

Solutions

Expert Solution

Solution:

Given:

Mean height = inches

Standard deviation =

Sample size = n = 22

We have to find: percentage of all samples of 22 of​ today's women in their 20s have mean heights of at least 65.74 ​inches

That is:

Find z score:

Thus

Look in z table for z = 2.8 and 0.04 and find area.

Thus we get: P( Z < 0.9977 )

thus

Thus 0.23 % of all samples of 22 of​ today's women in their 20s have mean heights of at least 65.74 ​inches.

orchestra answered 3 years ago
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