A binomial distribution has p = 1/3 and q = 2/3.How large a sample (n)is necessary to satisfy the criterion for using the normal approximation?
A)10
B)15
C)27
D)30

Question

A binomial distribution has p = 1/3 and q = 2/3.How large a sample (n)is necessary to satisfy the criterion for using the normal approximation?​
A)​10
B)​15
C)​27
D)​30

Quizplus · Accepted Answer

For the normal approximation to be valid, both np and nq must be greater than or equal to 10:
np = n * p = n * 1/3
nq = n * q = n * 2/3
We need to solve for "n" to find the smallest integer value that satisfies both inequalities:
np ≥ 10
n * 1/3 ≥ 10
n ≥ 10 / (1/3)
n ≥ 30
nq ≥ 10
n * 2/3 ≥ 10
n ≥ 10 / (2/3)
n ≥ 15
The smallest integer value that satisfies both inequalities is 30, so the answer is D.

A Binomial Distribution Has P = 1/3 and Q =