Question

Heights of men on a baseball team have a​ bell-shaped distribution with a mean of 166 cm 166 cm and a standard deviation of 5 cm 5 cm. Using the empirical​ rule, what is the approximate percentage of the men between the following​ values? a. 156 156 cm and 176 176 cm b. 151 151 cm and 181 181 cm

Answer 1

Answer:

95 %

99.7 %

Explanation:

$\mu$ = 166 cm = Mean

$\sigma$ = 5 cm =  Standard deviation

a) 156 cm and 176 cm

$166-5\times 2=156$

$166+5\times 2=176$

From the empirical rule 95% of all values are within 2 standard deviation of the mean, so about 95% of men are between 156 cm and 176 cm.

b) 151 cm and 181 cm

$166-5\times 3 =151$

$166+5\times 3=181$

The empirical rule tells us that about 99.7% of all values are within 3 standard deviations of the mean, so about 99.7% of men are between 151 cm and 181 cm.