Question

determine whether the normal sampling distribution can be used. the claim is p < 0.25 and the sample size is n = 18. do not use the normal distribution. use the normal distribution.

Explanation:

Step1: Recall Normal Approximation Conditions

To use the normal sampling distribution for a proportion, we check \( np \geq 5 \) and \( n(1 - p) \geq 5 \). Here, \( n = 18 \), \( p = 0.25 \).

Step2: Calculate \( np \) and \( n(1 - p) \)

• Calculate \( np \): \( np = 18 \times 0.25 = 4.5 \)
• Calculate \( n(1 - p) \): \( n(1 - p)=18\times(1 - 0.25)=18\times0.75 = 13.5 \)

Since \( np = 4.5 < 5 \), the condition \( np \geq 5 \) is not met. So we do not use the normal distribution.

Answer:

Do not use the normal distribution.