seventyeight percent of US homes have a telephone answering

seventy-eight percent of U.S. homes have a telephone answering device. In a random sample of 250 homes, what is the probability that fewer than 50 do not have a telephone answering device?

Solution

p = 1 - 0.78 = 0.22
mu = 0.22*250 = 55
sd = sqrt(250*0.22*(1-0.22)) = 6.5498

z = (50 - 55)/6.5498 = -0.7634

P(x < 50) = P(z < -0.7634)
= 0.2226 (Ans.)