Suppose the monthly unpaid balance on a Citicorp Mastercard is normally distributed with a mean of $1200 and standard deviation of $240. We want to show that the sample mean X̄ is an unbiased estimate of the population mean jz, and the sample variance s* is an unbiased estimate of the population variance σ² Note that you can generate observations from CITICORP accounts by using the formula =NORMINV(RAND(),1200,240). Develop a simulation as follows:

Generate 50 samples of five credit card balances each. Then freeze the random numbers. m™ 

Calculate X̄ and s² for each sample.

Show that the X̄’s average to a value near the actual mean of $1200.

Show that the s^2’s average to a value near the true value σ² = 240°.