Question

The Central Limit Theorem says that when sample size n is taken from any population with mean μ and standard deviation σ when n is large, which of the following statements are false? (4 points)
I The distribution of the sample mean is exactly Normal.
II The distribution of the sample mean is approximately normal.
III The standard deviation is equal to that of the population.
IV The distribution of the population is exactly Normal.

I and II

I only

II and III

II only

Answer 1

The option that is correct about the central limit theorem is D (II only).

What is the Central Limit theorem?

According to the central limit theorem, if you have a population with a mean and standard deviation and take sufficiently large random samples from it with replacement, the distribution of the sample means will be nearly normally distributed.

As we know about the central limit theorem, the distribution of the sample means is approximately normal. Therefore, the option that is correct about the central limit theorem is D (II only).

Learn more about Central Limit Theorem:

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