1. Given a population consisting of: 2, 3, 4, 6, 8, 9, 10; how many samples of size 3 are possible?
2. Given a population consisting of: 1, 3, 4, 6, 7, 8, 9; list All possible samples of size 2. Compute the mean of each sample. Calculate the population mean and compare it to the mean of the sample means.
3. Information from the American Institute of Insurance indicates the mean amount of life insurance per house hold in the US is $110,000. This distribution is positively skewed. The standard deviation of the population is $40,000.
a. What is the standard error of the mean?
b. Suppose you selected 50 samples of households. What is the expected shape of the distribution of the sample mean?
c. What is the likelihood of selection 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.