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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.)

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Answer:

a) 99.7%

b) 68%

Explanation:

[tex]\mu[/tex] = Mean = 168 cm

[tex]\sigma[/tex] = Standard deviation = 6 cm

a. 150 cm and 186 cm

[tex]168-6\times 3=150[/tex]

[tex]168+6\times 3=186[/tex]

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

b. 162 cm and 174 cm

[tex]168-6\times 1=162[/tex]

[tex]168+6\times 1=174[/tex]

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

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