Heights of men on a baseball team have a bell-shaped distribution with a mean of

Question

Heights of men on a baseball team have a bell-shaped distribution with a mean of 167 cm and a standard deviation of 5 cm.

Using the empirical rule, what is the approximate percentage of the men between the following values?

a.152cm and 182cm

b.157cm and177cm

a.____% of the men are between 152cm and 182cm.

(Round to one decimal place as needed.)

b.____% of the men are between 157cm and 177cm.

(Round to one decimal place as needed.)

______________________________________________________

(Need help with this problem as well; please and thank you.)

A survey found that women's heights are normally distributed with mean 63.8 in and standard deviation 2.4in. A branch of the military requires women's heights to be between 58 in and 80in.

a. Find the percentage of women meeting the height requirement. Are many women being denied the opportunity to join this branch of the military because they are too short or too tall?

b. If this branch of the military changes the height requirements so that all women are eligible except the shortest 1% and the tallest 2%, what are the new height requirements?

a. The percentage of women who meet the height requirement is_____%.(Round to two decimal places as needed.)

Are many women being denied the opportunity to join this branch of the military because they are too short or too tall?

A.Yes, because the percentage of women who meet the height requirement is fairly large.

B.Yes, because a large percentage of women are not allowed to join this branch of the military because of their height.

C.No, because only a small percentage of women are not allowed to join this branch of the military because of their height.

D.No, because the percentage of women who meet the height requirement is fairly small.

b. For the new height requirements, this branch of the military requires women's heights to be at least______in and at most______in.

(Round to one decimal place as needed.)

Explanation / Answer

Using the empirical rule 95% of the men are between the following values:

-2 and +2

167-2*5=157 and 167+2*5=177

Similarly, 99.7% of the men are between the following values:

-3 and +3

167-3*5=152 and 167+3*5=182

a.__99.7%__% of the men are between 152cm and 182cm.

b.__95%__% of the men are between 157cm and 177cm.

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