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.)
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