Question

Heights of men on a baseball team have a bell shaped distribution with a 171cm and a standard deviation of 8cm. Using the empirical rule, what is the approximate percentage of the men between the following:

163cm and 179cm

155cm and 187cm

Answer 1

Given $\mu =171$ and $\sigma =8$

a) $Z_{1}=\frac{X_{1}-\mu }{\sigma }=\frac{163-171}{8}=\frac{-8}{8}=-1$

$Z_{2}=\frac{X_{2}-\mu }{\sigma }=\frac{179-171}{8}=\frac{8}{8}=1$

$P(163< X< 179)=P(-1< Z< 1)=68\%$

b)$Z_{1}=\frac{X_{1}-\mu }{\sigma }=\frac{155-171}{8}=\frac{-16}{8}=-2$

$Z_{2}=\frac{X_{2}-\mu }{\sigma }=\frac{187-171}{8}=\frac{16}{8}=2$

$P(155< X< 187)=P(-2< Z< 2)=95\%$