A sample of 25 observations is taken from an infinite population. The sampling distribution of is A) not normal since n 30 and n1-P) 30

Question

A sample of 25 observations is taken from an infinite population. The sampling distribution of is
A) not normal since n < 30
B) approximately normal because is always normally distributed
C) approximately normal if np ≥ 5 and n1-P) ≥ 5
D) approximately normal if np > 30 and n1-P) > 30

Quizplus · Accepted Answer

According to the Central Limit Theorem, the sampling distribution of the sample mean will be approximately normal if the sample size is large enough and if certain conditions are met. These conditions include np ≥ 5 and n(1-P) ≥ 5, where n is the sample size and p is the probability of success. In this case, we do not have information about the value of p, but we can assume that the population is infinite. Therefore, we can use the conservative estimate of p = 0.5 to calculate the minimum sample size that satisfies the conditions. Plugging in the values, we get np = 25(0.5) = 12.5 and n(1-P) = 25(0.5) = 12.5, which both exceed the minimum threshold of 5. Therefore, we can conclude that the sampling distribution of the sample mean is approximately normal.

A Sample of 25 Observations Is Taken from an Infinite