Please eplain 3 The heights of women 20 to 29 are approxima

Please eplain :)

3. The heights of women 20 to 29 are approximately Normally distributed with mean 64.3 inches and
standard deviation 2.7 inches. Men in the same age group have mean height 69.9 inches with
standard deviation 3.1 inches.
a) What does it mean to be an “unusually short” woman?
b) How tall or short would a man be who is considered an outlier?

Solution

a)

Unusual values are more than 2 standard deviations from the mean.

Thus, an unusually short woman is less than

u - 2*sigma = 64.3 - 2*2.7 = 58.9 inches

[ANSWER: less than 58.9 in]

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b)

Unusual values are more than 2 standard deviations from the mean.

Thus,

u - 2*sigma = 69.9 - 2*3.1 = 63.7
u + 2*sigma = 69.9 + 2*3.1 = 76.1

Thus, an outlier is any man shorter than 63.7 in or taller than 76.1 in. [ANSWER]