Question

The normal approximation of the binomial distribution is appropriate when

np ≥ 5.

n(1 − p) ≥ 5.

np ≤ 5.

n(1 − p) ≤ 5 and np ≤ 5.

np ≥ 5 and n(1 − p) ≥ 5.

Answer 1

np ≥ 5 and n(1 − p) ≥ 5.

By using some mathematics it can be shown that there are a few conditions that we need to use a normal approximation to the binomial distribution. The number of observations n must be large enough, and the value of p so that both np and n(1 - p) are greater than or equal to 5. This is a rule of thumb, which is guided by statistical practice. The normal approximation can always be used, but if these conditions are not met then the approximation may not be that good of an approximation.