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The heights of 1000 students are approximately normally distributed with a mean of 174.5 centimeters and...

The heights of 1000 students are approximately normally distributed with a mean of 174.5 centimeters and a standard deviation of 6.9 centimeters. Suppose 200 random samples of size 25 are drawn from this population and the means recorded to the nearest tenth of a centimeter. Determine (a) the mean and standard deviation of the sampling distribution of X¯; (b) the number of sample means that fall between 171 and 177 cm.

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Answer #1

We are given:

(a)

and

(b)

The following information has been provided:
μ=174.5, σ=1.38

We need to compute Pr(171≤X≤177).

Therefore we get:

Number of sample means that fall between 171 and 177 = 0.9594 * 200 = 191.88 ~ 192

Excel Formula
NORM.DIST(177,174.5,1.38,TRUE)-NORM.DIST(171,174.5,1.38,TRUE)
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