Question

Describe the sampling distribution of p Assume the size of the population is 25,000. n=300​, p=0.3 Question content area bottom

Part 1
Choose the phrase that best describes the shape of the sampling distribution of p below.
A.Approximately normal because
n≤0.05N and np(1−p)<10.
B.Approximately normal because
n≤0.05N and np(1−p)≥10.
C.Not normal because
n≤0.05N and np(1−p)<10.
D.Not normal because
n≤0.05N and np(1−p)≥10.

Answer 1

The shape of the sampling distribution of p can be determined by the values of n and p(1-p). In this case, n = 300 and p = 0.3. The shape is approximately normal because np(1-p) is greater than 10.

Step-by-step explanation:

The shape of the sampling distribution of p can be determined by the values of n and p(1-p). In this case, n = 300 and p = 0.3. To determine the shape, we need to check if np(1-p) is less than 10 or greater than or equal to 10. If it is less than 10, the sampling distribution is not normal. If it is equal to or greater than 10, the sampling distribution is approximately normal. In this case, since 300 * 0.3 * (1-0.3) = 63, which is greater than 10, the shape of the sampling distribution of p is approximately normal. Therefore, the correct answer is option B.