A binomial distribution has p = 4/5.How large a sample would be necessary to justify using the normal approximation to the binomial distribution?
A)at least 10
B)at least 13
C)at least 40
D)at least 50

Question

A binomial distribution has p = 4/5.How large a sample would be necessary to justify using the normal approximation to the binomial distribution?​
A)​at least 10
B)​at least 13
C)​at least 40
D)​at least 50

Quizplus · Accepted Answer

According to the rule of thumb, the normal approximation to a binomial distribution is appropriate if np ≥ 10 and n(1-p) ≥ 10. Therefore, we need to find n such that np and n(1-p) both exceed 10. If p = 4/5, then (1-p) = 1/5. Solving for n, we get:
np ≥ 10
(4/5)n ≥ 10
n ≥ 12.5
n(1-p) ≥ 10
(1/5)n ≥ 10
n ≥ 50
Therefore, the minimum sample size required to justify using the normal approximation to the binomial distribution is 50. Hence, option D is correct.

A Binomial Distribution Has P = 4/5