A random sample of n = 36 scores is selected from a population.Which of the following distributions will definitively be normal?
A)The scores in the sample will form a normal distribution.
B)The scores in the population will form a normal distribution.
C)The distribution of sample means will form a normal distribution.
D)None of the distributions - the sample, the population, the distribution of sample means - will definitely be normal.

Question

A random sample of n = 36 scores is selected from a population.Which of the following distributions will definitively be normal?​
A)​The scores in the sample will form a normal distribution.
B)​The scores in the population will form a normal distribution.
C)​The distribution of sample means will form a normal distribution.
D)​None of the distributions - the sample, the population, the distribution of sample means - will definitely be normal.

Quizplus · Accepted Answer

According to the Central Limit Theorem, the distribution of sample means will approach a normal distribution as the sample size increases, regardless of the distribution of the population from which the sample is drawn. Therefore, the distribution of sample means will definitely be normal if the sample size is large enough (typically n ≥ 30). The other options do not definitively guarantee a normal distribution.

A Random Sample of N = 36 Scores Is Selected