Data indicate the mean amount of life insurance per household in the U.S is $110,000. Assume that the amount of life insurance per household is normally distributed with a standard deviation of $40,000.

A) If we select a random sample of 50 households, what is the standard error of the mean?

B) 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) What is the likelihood of selecting a sample with a mean of more than $100,000 but less than $112,000?