Suppose 40% of all college students have a computer at home and a sample of 64 is taken. What is the probability that more than 30 of those in the sample have a computer at home?
A) 0.3686
B) 0.1314
C) 0.8686
D) 0.6314
E) 0.1343

Question

Quizplus · Accepted Answer

The problem can be solved using the normal approximation to the binomial distribution. The mean is np = 64 * 0.4 = 25.6 and the standard deviation is sqrt(np(1-p)) = sqrt(64 * 0.4 * 0.6) = 3.92. We find the z-score for 30.5 (continuity correction) and use the standard normal distribution to find the probability. The probability of more than 30 is 1 - P(X ≤ 30), which is approximately 0.1314.

Suppose 40% of All College Students Have a Computer at Home