The Census Bureau reports that 82 of Americans over the age

The Census Bureau reports that 82% of Americans over the age of 25 are high school graduates. A survey of randomly selected residents of certain county included 1250 who were over the age of 25, and 998 of them were high school graduates.

(a) Find the mean and standard deviation for the number of high school graduates in groups of 1250 Americans over the age of 25.

Mean =

Standard deviation =

Solution

The Census Bureau reports that 82% of Americans over the age of 25 are high school graduates. A survey of randomly selected residents of certain county included 1250 who were over the age of 25, and 998 of them were high school graduates.

(a) Find the mean and standard deviation for the number of high school graduates in groups of 1250 Americans over the age of 25.

n=1250

p=0.82

Expectation = np = 1025

Variance = np(1 - p) = 184.5

Standard deviation = 13.5831

Mean =1025

Standard deviation = 13.5831

b) Is that county result of 998 unusually high, or low, or neither? (Here high means more than two standard deviations above the mean and similarly for low.)
(Enter HIGH or LOW or NEITHER)

mean-2*sd = 1025-2*13.5831 = 997.834

the value 998 is higher than mean-2*sd =997.834

The answer is NEITHER