Question

Many samples are the same size are taken from a population with a population proportion of 0.75. Which sample sizes, n, would be too small to use a normal curve to approximate the sampling distribution? Select all that apply.

A. 18
B. 30
C. 45
D. 60

Answer 1

To determine the minimum sample size required to use a normal curve to approximate the sampling distribution, we can use the formula n * p >= 5 and n * (1 - p) >= 5, where n is the sample size and p is the population proportion.

Given that the population proportion is 0.75:

A. 18
18 * 0.75 = 13.5 (greater than or equal to 5) - APPROVED

B. 30
30 * 0.75 = 22.5 (greater than or equal to 5) - APPROVED

C. 45
45 * 0.75 = 33.75 (greater than or equal to 5) - APPROVED

D. 60
60 * 0.75 = 45 (greater than or equal to 5) - APPROVED

Therefore, all of the sample sizes provided are large enough to use a normal curve to approximate the sampling distribution.