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Statistics - Sampling Methods and Central Limit Theorem

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"Information from the American Institute of Insurance indicates the mean amount of life insurance per household in the United States is $110,000. This distribution follows the normal distribution with a standard deviation of $40,000.
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"a. If we select a random sample of 50 households, what is the standard error of the mean?
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"b. What is the expected shape of the distribution of the sample mean?
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"c. What is the likelihood of selecting a sample with a mean of at least $112,000?
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"d. What is the likelihood of selecting a sample with a mean of more than $100,000?
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"e. Find the likelihood of selecting a sample with a mean of more than $100,000 but less
than $112,000.
"

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