Use the normal approximation to the binomial to find that probability for the specific value of X.
N = 20, p = 0.3, X = 7
A) 0.17
B) 0.35
C) 0.11
D) 0.3

Question

Quizplus · Accepted Answer

To use the normal approximation to the binomial, we need to check if the conditions are met: - np = 20*0.3 = 6 > 5 - n(1-p) = 20*0.7 = 14 > 5 Both conditions are met, so we can approximate the binomial distribution with a normal distribution with mean μ = np = 20*0.3 = 6 and standard deviation σ = sqrt(np(1-p)) = sqrt(20*0.3*0.7) = 1.8. To find P(X=7), we need to find the probability that a normal distribution with mean μ = 6 and standard deviation σ = 1.8 has a value between X=6.5 and X=7.5: z1 = (6.5 - 6)/1.8 = 0.28 z2 = (7.5 - 6)/1.8 = 0.83 Using a standard normal table, we find that P(0.28 < Z < 0.83) = P(Z < 0.83) - P(Z < 0.28) = 0.7967 - 0.6103 = 0.1864 Therefore, P(X=7) is approximately 0.1864, which is closest to choice A (0.17).

Use the Normal Approximation to the Binomial to Find That