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QUESTION

# The heights of young women are approximately normal with mean 65 inches and standard deviation 2.5 inches. The heights of men in the same age group have mean (and median) 70 inches. ?

The heights of young women are approximately normal with mean 65 inches and standard deviation 2.5 inches. The heights of men in the same age group have mean (and median) 70 inches.

a) What percentage of women are taller than a man of median height? b) What percentage of women are taller than 70 inches ? c) How to find between what heights do the middle 95% of women fall ? d) What percentage of women are shorter than 62.5 inches ?

For women you are given the standard deviation sigma=2.5 inches and the mean mu=65 inches. For men, you are given only the mean (and median), which is 70 inches.

a) Since the mens mean lies 3 standard deviations away, we know that 99.7% of women are shorter than 70 inches, so only 0.3% are taller than a man of median height.

c) The middle 95% of women lie within 2 standard deviations. Since the mean is located at 62.5, these women lie between 57.5=62.5-5 and 67.5=62.5+5 inches.
d) 50%  of women are shorter than 62.5 inches because 62.5 is the mean.