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 1330 who were over the age of 25, and 1086 of them were high school graduates.
(a) Find the mean and standard deviation for the number of high school graduates in groups of 1330 Americans over the age of 25.
Mean =
Standard deviation =
(b) Is that county result of 1086 unusually high, or low, or neither?
(Enter HIGH or LOW or NEITHER)

Solution

p0 = 0.82
x = 1086 , n = 1330 , phat=x/n = 0.817

a.
mean = np0 = 1330*0.82
= 1090.6

standard deviation = sqrt(np0(1-p0))
= sqrt(1330*0.82*0.18)
= 14.01

b.
we say that an event with a probability less than 5% is unusual

P(X< 1086 ) = P(Z< ((1086-1090.6) / 14.01)
= P(Z< -0.33 )
= 1 - P(Z<0.33)
= 1 - 0.6293
= 0.3707
= 37.07%

country result of 1086 is NEITHER unusually high nor low