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A large population of 5,000 students take a practice test to prepare for a standardized test. The population mean is 150 questions correct, and the standard deviation is 90.
(a) Let X = The number of questions correct obtained by a student. What is the mean and the standard deviation of X?
(b) Let X = The average number of questions correct in a sample of 120 students. What is the mean and the standard deviation of X ? By the Central Limit Theorem, what is the distribution of X ?
(c) What sample size should a researcher take to get a distribution of means of the samples with a standard deviation of 5?
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