EXAMPLE 18 Heights of American Women: Application of the 68-95-99.7 Rule

The heights of women between the ages of 18 and 24 are distributed roughly normally, with a mean of 64.5 inches and a standard deviation of 2.5 inches. Two standard deviations are 5 inches for this distribution. The "95" part of the 68-95-99.7 rule says that the middle 95% of young women are between and inches tall; that is, between 59.5 inches and 69.5 inches.

Keep in mind that this is only an approximation because the distribution of young women’s heights is approximately normal.

The other 5% of American women have heights outside the range from 59.5 to 69.5 inches. Because the normal distributions are symmetric, half of these women are on the tall side and half on the short side. So the tallest 2.5% of young women are taller than 69.5 inches.

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