Question

A sample of 32 observations is taken from an infinite population. The sampling distribution of a.is approximately normal because of the central limit theorem. b.is approximately normal because the sample size is small in comparison to the population size. c.is approximately normal because is always approximately normally distributed. d.cannot be determined

Answer 1

a.is approximately normal because of the central limit theorem.

Explanation:

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean
`\mu` and standard deviation
`\sigma`, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean
`\mu` and standard deviation
`s = (\sigma)/(√(n))`.

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

In this question:

Sample limit of 32 > 30, so the distribution is approximately normal because of the central limit theorem, and the correct answer is given by option a.