Suppose that the ATM amount may vary in addition to the random inter arrivals used above. In this case, 50% of the time $30 is withdrawn, 30% of the time $50 is withdrawn, and 20% of the time, $100 is withdrawn. Compute the mean and the variance of this distribution. Then, using Excel, make at least 10 replications of the monthly total amount withdrawn when (a) the ATM amount is always $50 and (b) the case that the ATM amount is random according to the distribution. Compute the average and the standard deviation of the monthly ATM amount withdrawn (sums) for the two cases using the replications that you obtain.