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Question

The heights of adult men in America are normally distributed with a mean of 69.4 inches and a standard deviation of 2.69 inches. The heights of adult women in America are also normally distributed, but with a mean of 64.4 inches and a standard deviation of 2.53 inches.

A) if a man is 6‘,3“ tall what is his Z score? (Two decimal places.)?

Z=

B) if a woman is 5‘11“ tall what is her Z score (to two decimal places)

C) who is relatively taller?

The 6‘3“ American man or 5’11” American woman?

Answer 1

Let "x" represent the observed value, let "μ" represent the mean, and let "σ" represent the standard deviation. Then the equation for the z-sore is:

So, first calculate the man's height in inches: 6 ft = (6)(12) = 72 inches plus the additional 3 inches gives us 75 inches. Plugging this into the equation with the mean and standard deviations for men:

z = (75 - 69.4)/2.69 = 5/6/2.69 = 2.08

So the z-score for the man is 2.08

For the woman, again calculate height in inches: 5 ft = (5)(12) = 60 inches plus the additional 11 inches gives us 71 inches. Plugging this into the equation with the mean and standard deviations for women:

z = (71 - 64.4)/2.53 = 6/6/2.53 = 2.61

So the z-score for the woman is 2.61

The z-score tells us that the woman, with the larger z-score, has a height that is farther away from the mean than the man therefore she is "relatively" taller.