Question

Heights of men on a baseball team have a​ bell-shaped distribution with a mean of 176 cm and a standard deviation of 7 cm.

Using the empirical​ rule, what is the approximate percentage of the men between the following​ values?

a.169 cm and 183 cm

b.162 cm and190 cm

Answer 1

mean = 176 , s = 7

a)

The key to solving this problem is to recognize that 169 and 183 are each exactly 1 standard deviation away
from the mean of 176. Therefore, 1 standard deviation from the mean is

176 - 7 = 169 cm
176 + 7 = 183 cm

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 172 cm and 186 cm.

b)

The key to solving this problem is to recognize that 162 and 190 are each exactly 2 standard deviations
away from the mean of 176. Therefore, 3 standard deviations from the mean is
176 − 2 ∙ 7 = 162,
176 + 2 ∙ 7 = 190.
The empirical rule tells us that about 95% of all values are within 2 standard deviations of the mean,
so about 95% of men are between 162cm and 190 cm.