State Farm Insurance has developed the following table to describe the distribution of automobile collision claims paid during the past year. a. Set up a table of intervals of random numbers that can be used with the Excel VLOOKUP function to generate values for automobile collision claim payments. b. Construct a simulation model to estimate the average claim payment amount and the standard deviation in the claim payment amounts. c. Let X be the discrete random variable representing the dollar value of an automobile collision claim payment. Let, x,, X2, . . x, represent possible values of X. Then, the mean (u) and standard deviation (o) of X can be computed as u = x, P(X = x,) + + x, x P(X = x,), and o = J(x, - ) x P(X = x,) + + (x, - u) X P(X = x,). Compare the val- ues of sample mean and sample standard deviation in part (b) to the analytical cal- culation of the mean and standard deviation. How can we improve the accuracy of the sample estimates from the simulation? Payment($) Probability 0.83 500 0.06 1,000 0.05 2,000 0.02 5,000 0.02 8,000 0.01 10,000 0.01