Sixty percent of a company's customers are females.What is the probability that a random sample of 200 customers is greater than 64 percent female?
A) 0.1229
B) 0.1556
C) 0.1898
D) .02158
E) 0.2847

Question

Quizplus · Accepted Answer

The probability can be calculated using the normal approximation to the binomial distribution. The mean is np = 200 * 0.6 = 120, and the standard deviation is sqrt(np(1-p)) = sqrt(200 * 0.6 * 0.4) = 6.93. We want P(X > 128), where 128 is 64% of 200. Using the normal approximation, we find the z-score: (128 - 120) / 6.93 = 1.154. Using the standard normal distribution table, P(Z > 1.154) ≈ 0.1229.

Sixty Percent of a Company's Customers Are Females