The distribution of heights of young women aged 18 to 24 is approximately normal with a mean of 64.5 inches and a standard deviation of 2.5 inches. Between what two heights do the middle 95% of women fall?

Question

The distribution of heights of young women aged 18 to 24 is approximately normal with a mean of 64.5 inches and a standard deviation of 2.5 inches.  Between what two heights do the middle 95% of women fall?

kropot72 · Answer

The empirical rule for a normal distribution states that approximately 95% of the data points lie within the range of plus and minus two standard deviations of the mean. Can you see how to use the empirical rule to find the required two heights?

anonymous · Answer

i dont even know what the empirical rule is

agent0smith · Answer

Well, 95 percent of them will lie within 2 standard deviations, above or below the mean.

The mean is 64.5, so add 2 SD's to find the upper limit
subtract 2 SD's to find the lower limit

anonymous · Answer

ugh i dont understand :(

agent0smith · Answer

mean of 64.5 inches... add 2 times the std dev to that (std dev is 2.5)

phi · Answer

They are asking for the area under the curve, starting in the middle, and going both to the left and the right

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