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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.

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8 A telephone survey utilized a sampling frame of 2000 numbers, and had a response rate of 25%. A question asked respondents if they preferred Brand 1, Brand 2, or Brand 3. According to the company, 35% of their customers preferred Brand 1, ...

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.