State Farm Insurance has developed the following table to describe the distribution of automobile collision claims...

 

 

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

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a We calculate the cumulative probability and set up the table in excel as below b we will use th... View the full answer