the central limit theorem is important in statistics because a) for any size sam

Question

the central limit theorem is important in statistics because
a) for any size sample, it says the sampling distribution of the sample mean is approximately normal.
b) for a large n, it says the population is approximately normal
c) for any population, it says the sampling distribution of the sample mean is approximately normal, regardless of the sample size
d) for a large n, it says the sampling distribution of the sample mean is approximately normal, regardless of the shape of the distribution of the sample population

Explanation / Answer

The central limit theorem is important in statistics because

d) for a large n, it says the sampling distribution of the sample mean is approximately normal, regardless of the shape of the distribution of the sample population.

In probability theory, the central limit theorem states that, given certain conditions, the sample mean of a sufficiently large number of iterates of independent random variables, each with a well-defined expected value and well-defined variance, will be approximately normally distributed, regardless of the underlying distribution.

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