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Information from the American Institute of Insurance indicates that the mean amount of life insurance per...

Information from the American Institute of Insurance indicates that the mean amount of life insurance per household in the United States is $115,000 and standard deviation is $41,250.

a) If a random sample of 32 households are selected, what is the shape of the sampling distribution of the sample means?

b) Specify the mean and standard deviation of the sampling distribution of the sample means, for samples of size 32.

c) What is the probability that in a random sample of 32 households the mean cost of life insurance is at least $111,000?

d) What is the probability that in a random sample of 32 households the mean cost of life insurance is at most $108,000?

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