Information from the American Institute of Insurance indicates the meanamount of life insurance per household in the United States is $110,000. This distribution is positively skewed. The standard deviationof the population is not known.

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

a) The standard error of mean = Standard deviation of population / square root of sample size

=40000/(50)^0.5=5656.854249

b) The sample mean will have a normal …

Solution explains the steps in finding out the standard error of insurance means when population standard deviation is not known. Probabilities for various sample means have also been worked out.