Question

18. Heights of men on a baseball team have a​ bell-shaped distribution with a mean of 186 cm and a standard deviation of 9 cm. Using the empirical​ rule, what is the approximate percentage of the men between the following​ values?

a. 159 cm and 213 cm

b. 168 cm and 204 cm

____ % of the men are between 159 cm and 213 cm.

____% of the men are between 168 cm and 204 cm.

Answer 1

Mean, $\mu$ = 186

Standard deviation, $\sigma$ = 9

a) Percentage of the mean between 159 and 213 = P(159<X<213)

$=P\left (\frac{159-186}{9}<Z<\frac{213-186}{9} \right )$

$=P\left (-3<Z<3 \right )$

According to empirical rule about 99.7% of all values fall within 3 standard deviation of the mean.

99.7 % of the men are between 159 cm and 213 cm.

b) Percentage of the mean between 168 and 204 = P(168<X<204)

$=P\left (\frac{168-186}{9}<Z<\frac{204-186}{9} \right )$

$=P\left (-2<Z<2 \right )$

According to empirical rule about 95% of all values fall within 2 standard deviation of the mean.

95 % of the men are between 168 cm and 204 cm.