Question

The population of current statistics students has ages with mean muμ and standard deviation sigmaσ. samples of statistics students are randomly selected so that there are exactly 4242 students in each sample. for each​ sample, the mean age is computed. what does the central limit theorem tell us about the distribution of those mean​ ages?

Answer 1

We are told that the population has a mean of μ and standard deviation of σ.

From each sample of 42, we can compute a mean value of
`\Bar{x}`.
We do not know the distribution for any sample.

According to the Central Limit Theorem, the distribution of the sample means will follow a normal distribution, regardless of the distribution of the individual samples.

Answer:
The distribution of sample means is normally distributed, and
`\Bar{x} \Rightarrow \mu`,