SOLUTION: can someone please help me out with this problem? Heights of men on a baseball team have a​ bell-shaped distribution with a mean of 173 cm and a standard deviation of 6 cm

Algebra.Com
Question 1012090: can someone please help me out with this problem?
Heights of men on a baseball team have a​ bell-shaped distribution with a mean of 173 cm and a standard deviation of 6 cm. Using the empirical​ rule, what is the approximate percentage of the men between the following​ values?
a. 155 cm and 191 cm
b. 167 cm and 179 cm
a.
___​% of the men are between 155 cm and 191 cm.
​(Round to one decimal place as​ needed.)
b.
___% of the men are between 167 cm and 179 cm.
​(Round to one decimal place as​ needed.)

Answer by Theo(13342)   (Show Source): You can put this solution on YOUR website!
Heights of men on a baseball team have a​ bell-shaped distribution with a mean of 173 cm and a standard deviation of 6 cm. Using the empirical​ rule, what is the approximate percentage of the men between the following​ values?

a. 155 cm and 191 cm
b. 167 cm and 179 cm

a.
___​% of the men are between 155 cm and 191 cm.
​(Round to one decimal place as​ needed.)
b.
___% of the men are between 167 cm and 179 cm.
​(Round to one decimal place as​ needed.)

z-score = (raw-score minus mean) / standard deviation.

mean is 173 and standard deviation is 6.

z1a = (155 - 173)/6
z1b = (191 - 173)/6
z2a = (167 - 173)/6
z2b = (179 - 173)/6

solve for z in each of these equations to get:

z1a = -3
z1b = 3

z2a = -1
z2b = 1

the empirical rule says:

68% will fall within the first standard deviation, 95% within the first two standard deviations, and 99.7% will fall within the first three standard deviations of the mean.

It is also referred to as the Three Sigma Rule, or the 68-95-99.7 Rule.

your solutions are:

a.
99.7​% of the men are between 155 cm and 191 cm.
​(Round to one decimal place as​ needed.)

b.
68% of the men are between 167 cm and 179 cm.
​(Round to one decimal place as​ needed.)

RELATED QUESTIONS

Heights of men on a baseball team have a​ bell-shaped distribution with a mean of... (answered by Boreal)
Heights of men on a baseball team have a​ bell-shaped distribution with a mean of... (answered by stanbon)
Heights of men on a baseball team have a​ bell-shaped distribution with a mean of... (answered by Boreal)
Heights of men on a baseball team have a​ bell-shaped distribution with a mean of (answered by robertb)
Heights of men on a baseball team have a​ bell-shaped distribution with a mean of... (answered by robertb)
Heights of men on a baseball team have a bell shaped distribution with a mean of 169 cm... (answered by ewatrrr)
Heights of men on a baseball team have a bell shaped distribution with a mean of 170 cm... (answered by jim_thompson5910)
Correction to previous submission: Heights of men on a baseball team have a bell... (answered by stanbon)
Heights of men on a baseball team have a bell-shaped distribution with a mean of 167 cm... (answered by Boreal)