The Central Limit Theorem tells us that for population distribution(s), if we repeatedly take new random samples from this distribution and calculate the average each time, then: a. If you take a really large sample size you would expect the sample average to be b. If your sample size is small, the sample averages will be spread out. c. If your sample size is small, the distribution of the sample averages will look more like distribution. d. If your sample size is very large, the distribution of the sample averages will look more like distribution.

The central limit Theorem states that for population distribution if you repeatedly take samples from the distribution, then the normal thing for it to happen would be that the distribution means of the samples will be normally distributed, this is what it states, the option that comes closer to that statement would be d. If your sample size is very large, the distribution of the sample averages will look more like distribution, because they large sample will create for a normally distributed means distribution.

joaobezerra joaobezerra · Answer 2 · 2022-03-03T11:58:31+01:00

Using the Central Limit Theorem, the correct statement is:

If you take a really large sample size you would expect the sample average to be clustered around the population mean.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

Hence, a large sample leads to a small standard error, which means that the correct statement is:

If you take a really large sample size you would expect the sample average to be clustered around the population mean.

To learn more about the Central Limit Theorem, you can take a look at https://brainly.com/question/24663213