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Question: As the sample size n increases without limit, the shape of the distribution of the sample means taken with replacement from a population with mean μ and standard deviation σ will approach a normal distribution. This distribution will have mean μ and standard deviation σn.
In statistics, what is this statement referred to as?


A ) Correction factor for continuity
B ) Normal distribution
C ) The Central Limit Theorem
D ) Standard error of the mean

Steps to derive

1 The Central Limit Theorem:
As the sample size n increases without limit, the shape of the distribution of the sample means taken with replacement from a population with mean μ and standard deviation σ will approach a normal distribution. This distribution will have mean μ and standard deviation σn.

2 If the sample size increases, the central limit theorem can be used to answer the questions about the sample means.

3 Therefore, in statistics, the statement is reffered as 'The Central Limit Theorem'.



Hence the right answer is Option C

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