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# 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.

b) Same answer as (a).

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.