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

Answer:

a) 99.7%

b) 68%

Explanation:

$\mu$ = Mean = 168 cm

$\sigma$ = Standard deviation = 6 cm

a. 150 cm and 186 cm

$168-6\times 3=150$

$168+6\times 3=186$

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

b. 162 cm and 174 cm

$168-6\times 1=162$

$168+6\times 1=174$

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