Heights of men on a baseball team have a bellshaped distribu

Heights of men on a baseball team have a bell-shaped distribution with a mean of 179 cmmm and a standard deviation of 7cm. Using the empirical rule, what is the approximate percentage of the mean between the following values?

a)165 cm and 193 cm

b)158 cm and 200 cm

Solution

A)

As the number of standard deviations from the mean z is given by

z = (x - u)/sigma

Then for x = 193 cm,

z = (193-179)/7 = 2

Thus, from the empirical rule, 95% of the data lie in this interval. [ANSWER, 95%]

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B)

As the number of standard deviations from the mean z is given by

z = (x - u)/sigma

Then for x = 200 cm,

z = (200-179)/7 = 3

Thus, from the empirical rule, 99.7% of the data lie in this interval. [ANSWER, 99.7%]