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Sample mean probabilities with the central limit theorem

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Survey of 1976-80 found that the mean serum cholesterol level for U.S. males aged 20-74 years was 211. The standard deviation was approximately 90. Consider the sampling distribution of the sample mean based on samples of size 100 drawn from this population of males.

1. What are the mean of the sampling distribution?

2. What is the standard deviation of the sampling distribution?

3. Is it necessary for the original distribution to be normal? Explain this answer.

4. Suppose a random sample of 100 is taken, what is the probability that the mean serum cholesterol level will be between 198 and 220?

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Solution Summary

This solution finds probabilities related to a sample mean by applying the central limit theorem.