Question

Heights of men on a baseball team have a​ bell-shaped distribution with a mean of 166 cm166 cm and a standard deviation of 6 cm6 cm. Using the empirical​ rule, what is the approximate percentage of the men between the following​ values?a. 148148 cm and 184184 cm b. 160160 cm and 172172 cm

Answer 1

a) 89%; b) 68%

Explanation:

We know that a mean
`\mu=166` and a standard deviation is
`\sigma=6.`

a) Notice that 148 and 184 are each exactly 3 standard deviation away from the mean:

`(148-166)/(6)=-3\\ (184-166)/(6)=3\\`

So, we get that at least
`(1-((1)/(3) )^2)=89%` of the men has a height between 148 cm and 184 cm.

b) Notice that 160 and 172 are exactly 1 standard deviation away from the mean.

`(160-166)/(6)=-1\\\\(172-166)/(6)=1`

By the empirical rule , 68% of the men has a height between 160 cm and 172 cm.