According to Information Please Almanac 59 of males between

According to Information Please Almanac, 59% of males between the ages of 18 and 24 have lived at home in 1998. Suppose a survey is administered at a community college to 200 randomly selected male students between 18 and 24 years old. Approximate the probability that a survey would result in at least 135 of the respondants living at home.

Solution

mean= n*p=200*0.59 =118

standard deviation =sqrt(n*p*(1-p))

=sqrt(200*0.59*(1-0.59)) =6.955573

So the probability that a survey would result in at least 135 of the respondants living at home is

P(X>=135) = P((X-mean)/s >(135-118)/6.955573)

=P(Z>2.44) = 0.0073 (from standard normal table)