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SAT Scores and the Central Limit Theorem

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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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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.

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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, ...

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Changping Wang, MA
Education
  • BSc , Wuhan Univ. China
  • MA, Shandong Univ.
Recent Feedback
  • "Your solution, looks excellent. I recognize things from previous chapters. I have seen the standard deviation formula you used to get 5.154. I do understand the Central Limit Theorem needs the sample size (n) to be greater than 30, we have 100. I do understand the sample mean(s) of the population will follow a normal distribution, and that CLT states the sample mean of population is the population (mean), we have 143.74. But when and WHY do we use the standard deviation formula where you got 5.154. WHEN & Why use standard deviation of the sample mean. I don't understand, why don't we simply use the "100" I understand that standard deviation is the square root of variance. I do understand that the variance is the square of the differences of each sample data value minus the mean. But somehow, why not use 100, why use standard deviation of sample mean? Please help explain."
  • "excellent work"
  • "Thank you so much for all of your help!!! I will be posting another assignment. Please let me know (once posted), if the credits I'm offering is enough or you ! Thanks again!"
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