If x is a binomial random variable where n = 100 and p = .1,find the probability that x is less than or equal to 10,using the normal approximation to the binomial.
A).5675
B).0170
C).5714
D).4325

Question

Quizplus · Accepted Answer

The normal approximation to the binomial distribution can be used here. The mean (μ) is np = 100 * 0.1 = 10 and the standard deviation (σ) is sqrt(np(1-p)) = sqrt(100 * 0.1 * 0.9) = 3. The continuity correction factor is applied, so we find P(X ≤ 10.5). Using the standard normal distribution, this corresponds to a z-score of (10.5 - 10) / 3 = 0.1667. The probability corresponding to this z-score is approximately 0.5675.

If X Is a Binomial Random Variable Where N =