A sample of 92 observations is taken from an infinite population.The sampling distribution of Is approximately
A)normal because Is always approximately normally distributed
B)normal because the sample size is small in comparison to the population size
C)normal because of the central limit theorem
D)None of these alternatives is correct.

Question

A sample of 92 observations is taken from an infinite population.The sampling distribution of  Is approximately
A)normal because Is always approximately normally distributed 
B)normal because the sample size is small in comparison to the population size 
C)normal because of the central limit theorem 
D)None of these alternatives is correct.

Quizplus · Accepted Answer

The central limit theorem states that as the sample size increases, the sampling distribution of the sample mean approaches a normal distribution, regardless of the shape of the population distribution. Therefore, the sampling distribution of the sample mean in this case is approximately normal because the sample size is relatively large (92 observations). Option A is incorrect because the fact that the population is infinite does not guarantee a normal sampling distribution. Option B is incorrect because the sample size is not small in comparison to the population size. Option D is incorrect as option C is the correct explanation for this problem.

A Sample of 92 Observations Is Taken from an Infinite