# Central Limit Theorem and adjusted standard deviation

Per capita consumption of Spam in the US is Normally distributed with a mean of 2.3 pounds and a standard deviation of 0.9 pounds. Random sample of 20 people are chosen. Use the Central Limit Theorem to find the mean and standard error of the mean (adjusted standard deviation) for samples of size 20, or state why the Theorem does not apply.

I think that 20 is not a large enough population for the central limit theorem

## 1 Answer

If population SD is 0.9 pounds, the standard error of the mean (that is the standard deviation of $\bar X$) for $n=20$ is $0.9/\sqrt{20}.$ A formula for that must be just a few pages before this problem in the text.

It is true that the CLT is a limit theorem as $n\rightarrow\infty$. However, in some instances good approximations can be found for $n = 20$ or smaller. Does the text give any clue about that?

Perhaps more important here is to consider what limiting distribution the CLT promises. In this case you are told that the population is normal. What do you know about the distribution of the sample mean from a normal population? Do you think a theorem about limits is needed here?

I realize I am asking questions rather than giving answers. But you do not show much indication of having read the text before posting this. I am trying to encourage you to think before asking. If this is not enough help, then try editing your question to tell us more about what you know and what is bothering you.

Also, different texts include different things in their statements of the "CLT." Maybe quote us what the version in your text says.