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 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.