Given that X is a binomial random variable, then between which of the following values would the binomial probability P(X = x) be approximated by the area under a normal curve?
A) x - 0.5 and 0.0
B) 0.0 and x + 0.5
C) 1 - x and 1 + x
D) x - 0.5 and x + 0.5

Question

Quizplus · Accepted Answer

The general guideline for approximating a binomial distribution as a normal distribution is that the mean of the binomial distribution, μ = np, and the standard deviation of the binomial distribution, σ = sqrt(np(1-p)), should both be greater than or equal to 5. Thus, we want values of x that are close to the mean (np) of the distribution. Using the continuity correction (shifting the boundaries by 0.5), we get the range (x-0.5, x+0.5), which is closest to np. Choice D includes values of x within this range, and the other choices do not.

Given That X Is a Binomial Random Variable, Then Between