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SAT Scores and the Central Limit Theorem

Would you be able to baby step walk me through the formulas needed to solve this problem? ie; step 1, step 2, etc. Maybe you could use a similar problem to this one so I can at least understand the process I need to do to get this answer? This book I have does not simplify and step through the method for solving this in a way that I can understand. I have other similar questions, and if I understand this one I might be able to do the rest.

SAT Scores and the Central Limit Theorem. Assume that SAT scores are normally distributed with a mean of 500 and a standard deviation of 100. Suppose that many samples of size n are taken from a large population of students and the mean SAT score is computer for each sample. Find the mean and standard deviation of the resulting distribution of sample means for n = 100 and for n = 400. Briefly explain why the standard deviation is different for the two values of n.

Solution Summary

This solution uses the mean of the sample, standard deviation, and distribution to determine sample mean and deviation for n=100 and n=400. All steps are shown and brief explanations.