central limit theorem

Question

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.

Answer 1

Since you already know the population parameter is normally distributed, then it doesn't matter that the sample is relatively small, so the CLT applies. If the parameter was not normal, then you might need a larger sample to justify its use.

 

The calculation then is straightforward: the mean of the sample distribution is equal to the mean of the population (2.3), and the standard error of the means is equal to the st. dev. of the population divided by the square root of the sample size, or

 

0.9 / √20 = 0.20