Question

Heights of men on a baseball team have a bell-shaped distribution with a mean of 177 cm and a standard deviation of 6 cm. Using the empirical rule, what is the approximate percentage of the men between the following values? a. 171 cm and 183 cm b. 165 cm and 189 cm

Answer 1

a. The key to solving this problem is to recognize that 171 and 183 are each exactly 1 standard deviation away from the mean of 177. Therefore, 1 standard deviation from the mean is:

$\begin{gathered} 177-6=171 \\ 177+6=183 \end{gathered}$

The empirical rule tells us that about 68% of all values are within 1 standard deviation of the mean, so about 68% of men are between 171 cm and 183 cm.

b.