Question: 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 \(\bar{X}\) is an unbiased estimate of the population mean μ , and the sample variance s² is an unbiased estimate of the population variance σ². Note that you can generate observation from CITICORP accounts by using the formula

Develop a simulation as follows:

- Generate 50 samples of five credit card balances each. Do not freeze the random numbers

- Calculate \(\bar{X}\) and s² for each sample

- Show that \(\bar{X}\) average to a value near the actual mean of $1200

- Show that s²'s average to a value near the true value σ²=240².