Assume that x is a binomial random variable with n = 100 and p = 0.60. Use a normal approximation to find P(x ≤ 65).
A) 0.8686
B) 0.8212
C) 0.5910
D) 0.1314

Question

Quizplus · Accepted Answer

The correct answer is A because the normal approximation to the binomial distribution is accurate when np and n(1-p) are both greater than or equal to 5. In this case, np = 100 * 0.60 = 60 and n(1-p) = 100 * 0.40 = 40, so both conditions are met. The mean of the binomial distribution is np = 60 and the standard deviation is sqrt(np(1-p)) = sqrt(60 * 0.40) = 4.90. The z-score for x = 65 is (65 - 60) / 4.90 = 1.02. The probability of a z-score less than or equal to 1.02 is 0.8686, which is the correct answer.

Assume That X Is a Binomial Random Variable with N