Question

Heights of men on a baseball team have a bell-shaped distribution with a mean of 184cm and a standard deviation of 7cm. Using the empirical rule, what is the approximate percentage of the men between the following values?

a) 170cm and 198cm

b) 163cm and 205cm

Answer 1

Theory: The empirical rule states that 68% of all values will lie within 1 standard deviation of the mean, 95% within 2 standard deviations and 99.7% within 3 standard deviations.

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(a) 2 standard deviations = 7cm*2 = 14cm.

So, 14 cm within the mean = 184cm - 14cm to 184cm + 14cm = 170cm to 198cm

Hence, since 170cm to 198cm is within 2 standard deviations from the mean, 95% of the men's heights will lie in this range.

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(b) 3 standard deviations = 7cm*3 = 21cm.

So, 21 cm within the mean = 184cm - 21cm to 184cm + 21cm = 163cm to 205cm

Hence, since 163cm to 205cm is within 3 standard deviations from the mean, 99.7% of the men's heights will lie in this range.

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Please comment in case any additional clarification is needed. Thanks.