Assume that x is a binomial random variable with n = 400 and p = 0.30. Use a normal approximation to find P(x 100).
A) 0.9834
B) 0.9875
C) 0.5854
D) 0.5910

Question

Assume that x is a binomial random variable with n = 400 and p = 0.30. Use a normal approximation to find P(x > 100).
A) 0.9834
B) 0.9875
C) 0.5854
D) 0.5910

Quizplus · Accepted Answer

To use the normal approximation for a binomial distribution, we calculate the mean (np = 120) and standard deviation (sqrt(np(1-p)) = sqrt(84) ≈ 9.165). We then find the z-score for x = 100. Using continuity correction, we use x = 100.5. The z-score is (100.5 - 120) / 9.165 ≈ -2.13. Looking up this z-score in a standard normal distribution table gives a probability of approximately 0.9834 for P(x > 100).

Assume That X Is a Binomial Random Variable with N