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3. Information from the American Institute of Insurance indicates the mean amount of life insurance per household in the United States is $126,000. This distribution follows the normal distribution with a standard deviation of $40,000. (a) If we select a random sample of 64 households, what is the standard error of the mean? (b) What is the expected shape of the distribution of the sample mean? Explain why. (c) What is the likelihood of selecting a sample with a mean of at least $130,000?

3. Information from the American Institute of Insurance indicates the mean amount of life insurance per household in the United States is $126,000. This distribution follows the normal distribution with a standard deviation of $40,000. (a) If we select a random sample of 64 households, what is the standard error of the mean? (b) What is the expected shape of the distribution of the sample mean? Explain why. (c) What is the likelihood of selecting a sample with a mean of at least $130,000?

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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3. Information from the American Institute of Insurance indicates the mean amount of life insurance per household in the United States is $126,000. This distribution follows the normal distribution with a standard deviation of $40,000. (a) If we select a random sample of 64 households, what is the standard error of the mean? (b) What is the expected shape of the distribution of the sample mean? Explain why. (c) What is the likelihood of selecting a sample with a mean of at least $130,000? 3 (d) Find the likelihood of selecting a sample with a mean of more than $118,000 but less than $130,000.
Transcribed Image Text:3. Information from the American Institute of Insurance indicates the mean amount of life insurance per household in the United States is $126,000. This distribution follows the normal distribution with a standard deviation of $40,000. (a) If we select a random sample of 64 households, what is the standard error of the mean? (b) What is the expected shape of the distribution of the sample mean? Explain why. (c) What is the likelihood of selecting a sample with a mean of at least $130,000? 3 (d) Find the likelihood of selecting a sample with a mean of more than $118,000 but less than $130,000.
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