Under what circumstances does the binomial distribution approximate a normal distribution?
A)when pn 10
B)when qn 10
C)when pn and qn are both 10
D)when npq 10

Question

Under what circumstances does the binomial distribution approximate a normal distribution?​
A)​when pn > 10
B)​when qn > 10
C)​when pn and qn are both > 10
D)​when npq > 10

Quizplus · Accepted Answer

The binomial distribution approximates a normal distribution when both np and nq are greater than 10, where n is the number of trials, p is the probability of success, and q is the probability of failure (q = 1 - p). This condition ensures that there are enough occurrences of both outcomes (success and failure) for the distribution to be symmetric and bell-shaped, resembling a normal distribution.

Under What Circumstances Does the Binomial Distribution Approximate a Normal