# Positively Skewed Distribution: Life Insurance per Household

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 is positively skewed. The standard deviation of the population is not known.

A. a random sample of 50 household revealed a mean of $112,000 and a standard deviation of $40,000. What is the standard error of the mean?

B. Suppose that you selected 50 samples of households. What is the expected shape of the distribution of the sample mean?

C. What is the likelihood of selecting a sample with a mean of at least $112,000?

D. What is the likelihood of selecting a sample of more than 100,000?

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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#### Solution Preview

A. a random sample of 50 household revealed a mean of $112,000 and a standard deviation of $40,000. What is the standard error of the mean?

N = 50

M = 112000

SD = 40000

Standard error is SE = SD / SQRT(n) = 40000/SQRT(50)= 5,656.85

B. Suppose that you selected 50 samples of households. What is the expected ...

#### Solution Summary

This solution contains complete steps of calculations and brief explanations to determine standard error of the mean, expected shape of the distribution, and selecting sample with specific means.

Standard Error and the Mean of life insurance per household in the US

Each response must include your calculations.

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 is positively skewed. The standard deviation of the population is not known.

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Complete the following:

a A random sample of 50 households revealed a mean of $112,000 and a standard deviation of $40,000. What is the standard error of the mean?

b Suppose that you selected 50 samples of households. What is the expected shape of the distribution of the sample mean?

c What is the likelihood of selecting a sample with a mean of at least $112,000?

d What is the likelihood of selecting a sample with a mean of more than $100,000?

e Find the likelihood of selecting a sample with a mean of more than $100,000 but less than $112,000.