Assume that x is a binomial random variable with n = 1000 and p = 0.80. Use a normal approximation to find P(800

Question

Assume that x is a binomial random variable with n = 1000 and p = 0.80. Use a normal approximation to find P(800 < x ≤ 820).
A) 0.4314
B) 0.4222
C) 0.4474
D) 0.0517

Quizplus · Accepted Answer

The correct answer is A because the normal approximation to the binomial distribution is accurate when n is large and p is not too close to 0 or 1. In this case, n = 1000 and p = 0.80, so the normal approximation is appropriate. The mean of the binomial distribution is np = 1000 * 0.80 = 800, and the standard deviation is sqrt(np(1-p)) = sqrt(1000 * 0.80 * 0.20) = 11.28. Therefore, the z-score for x = 800 is (800 - 800) / 11.28 = 0, and the z-score for x = 820 is (820 - 800) / 11.28 = 1.78. The probability of 0 < z < 1.78 is 0.4314, which is the answer.

Assume That X Is a Binomial Random Variable with N