Question

explain how to decide when a normal distribution can be used to approximate a binomial distribution.

choose the correct answer below.

a. if np < 5 and nq < 5, the normal distribution can be used.

b. if np ≥ 5 and nq ≥ 5, the normal distribution can be used.

c. if np ≠ 5 and nq ≠ 5, the normal distribution can be used.

d. if np > 0 and nq > 0, the normal distribution can be used.

Explanation:

To determine when a normal distribution can approximate a binomial distribution, we use the rule that the normal approximation is appropriate when both \( np \geq 5 \) and \( nq \geq 5 \) (where \( n \) is the number of trials, \( p \) is the probability of success, and \( q = 1 - p \) is the probability of failure). Option A is incorrect because it uses \( < 5 \), option C is incorrect as it uses \(
eq 5 \), and option D is incorrect as it uses \( > 0 \) which is too lenient. Option B matches the correct rule.

Answer:

B. If \( np \geq 5 \) and \( nq \geq 5 \), the normal distribution can be used.