Question

Heights of men on a baseball team have a​ bell-shaped distribution with a mean of 168 cmand a standard deviation of 6 cm.Using the empirical​ rule, what is the approximate percentage of the men between the following​ values?a. 150cm and 186cmb. 162cm and 174cma. nothing​%of the men are between 150cm and 186cm.​(Round to one decimal place as​ needed.)b. nothing​%of the men are between 162cm and 174cm.​(Round to one decimal place as​ needed.)

Answer 1

a) 99.7%

b) 68%

Step-by-step explanation:

`\mu` = Mean = 168 cm

`\sigma` = Standard deviation = 6 cm

a. 150 cm and 186 cm

`168-6* 3=150`

`168+6* 3=186`

They vary by 3 standard deviations. So, 99.7% of men are between 150 and 186 cm

b. 162 cm and 174 cm

`168-6* 1=162`

`168+6* 1=174`

They vary by 1 standard deviations. So, 68% of men are between 162 and 174 cm