Question

determine whether the normal sampling distribution can be used. the claim is p ≤ 0.132 and the sample size is n = 48.

options:

• do not use the normal distribution.
• use the normal distribution.

Explanation:

Step1: Recall Normal Approximation Conditions

For a binomial distribution to be approximated by a normal distribution, we need \( np \geq 5 \) and \( n(1 - p) \geq 5 \). Here, \( n = 48 \) and \( p = 0.132 \).

Step2: Calculate \( np \)

\( np = 48\times0.132 = 6.336 \)

Step3: Calculate \( n(1 - p) \)

\( 1 - p = 1 - 0.132 = 0.868 \)
\( n(1 - p)=48\times0.868 = 41.664 \)

Step4: Check Conditions

Both \( np = 6.336\geq5 \) and \( n(1 - p)=41.664\geq5 \) are satisfied. So we can use the normal distribution.

Answer:

Use the normal distribution.