Problem: 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 follows the normal distribution with a standard deviation of $40,000.
Question 1: If we select a random sample of 50 households, what is the standard error of the mean?
Question 2: What is the expected shape of the distribution of the sample?
Question 3: What is the likelihood of selecting a sample with a mean of at least $112,000?
Question 4: What is the likelihood of selecting a sample with a mean of more than $100,000?
Question 5: Find the likelihood of selecting a sample with a mean of more than $100,000 but less than $112,000.