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WB8-4. Heights of women aged 18 to 24 years are approximately normal with a mean of 64.5 inches and a standard deviation of 2.5 inches. (a) Find an interval that contains all heights within 1 standard deviation of the mean.

Ask by Curry Munoz. in the United States
Feb 25,2025

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The interval is from 62 inches to 67 inches.

Solution

We are given that the heights follow a normal distribution with a mean of 64.5 inches and a standard deviation of 2.5 inches. To find the interval that contains all heights within 1 standard deviation of the mean, we calculate: Lower limit = Mean - 1(Standard Deviation) = 64.5 - 2.5 = 62 inches Upper limit = Mean + 1(Standard Deviation) = 64.5 + 2.5 = 67 inches Thus, the interval is from 62 inches to 67 inches.

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The Deep Dive

The interval that contains all heights within 1 standard deviation of the mean can be calculated by taking the mean and adding and subtracting the standard deviation. Hence, you add 2.5 inches to the mean of 64.5 inches, resulting in 67 inches, and subtract 2.5 inches from the mean, yielding 62 inches. Therefore, the interval is from 62 inches to 67 inches. So, the interval that contains all heights within 1 standard deviation of the mean is [62 inches, 67 inches].

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