It is estimated that 75 of all young adults between the ages

It is estimated that 75% of all young adults between the ages of 18-35 do not have a landline in their homes and only use a cell phone at home.

What is the probability that everyone in a simple random sample of 100 young adults owns a landline?

Solution

X: percent of 18-35 with no landline. Then X is a Bernoulli RV, with standard deviation sqrt(pq )= sqrt(.75*.25) = sqrt(.1875)=.433. To get the standard deviation of a sample of 100, we simply divide the standard deviation by the square root of 100; standard deviation is .433/10 = .0433.