Question 1113610: 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 2.97 inches. If the mean height today is the same as that of a half-century ago, what percentage of all samples of 23 of today's women in their 20s have mean heights of at least 65.65 inches?
About __% of all samples have mean heights of at least 65.65 inches.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! 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 2.97 inches.
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If the mean height today is the same as that of a half-century ago, what percentage of all samples of 23 of today's women in their 20s have mean heights of at least 65.65 inches?
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Note: std of the means of samples of size 23 = 2.97/sqrt(23) = 0.6193
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z(65.65) = (65.65-64.7)/0.6193 = 1.5340
p(u-bar >= 65.56) = p(z >= 1.5340) = normalcdf(1.5340,100) = 0.0625
About 6.25% of all samples have mean heights of at least 65.65 inches.
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Cheers,
Stan H.
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