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An Insurance company has developed the following table to describe the distribution of automobile collision claims paid during the past year. Payment ($) 0 500 average 1,000 2,000 5,000 8,000 10,000 Probability 0.85 0.06 0.03 0.02 0.02 0.01 0.01 (a) Set up a table of intervals of random numbers ranging from 0 to 1 that can be used with the Excel VLOOKUP function to generate values for automobile collision claim payments. Lower End of Interval Upper End of Interval Payment($) 0 500 1,000 2,000 5,000 8,000 10,000 (b) Construct a simulation model to estimate the average claim payment amount (in $) and the standard deviation (In $) in the claim payment amounts. (Use at least 1,000 trials. Round your answers to two decimal places.) 12:05 PM

An Insurance company has developed the following table to describe the distribution of automobile collision claims paid during the past year. Payment ($) 0 500 average 1,000 2,000 5,000 8,000 10,000 Probability 0.85 0.06 0.03 0.02 0.02 0.01 0.01 (a) Set up a table of intervals of random numbers ranging from 0 to 1 that can be used with the Excel VLOOKUP function to generate values for automobile collision claim payments. Lower End of Interval Upper End of Interval Payment($) 0 500 1,000 2,000 5,000 8,000 10,000 (b) Construct a simulation model to estimate the average claim payment amount (in $) and the standard deviation (In $) in the claim payment amounts. (Use at least 1,000 trials. Round your answers to two decimal places.) 12:05 PM

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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**Distribution of Automobile Collision Claims** An insurance company has developed the following table to describe the distribution of automobile collision claims paid during the past year. | Payment ($) | Probability | |-------------|-------------| | 0 | 0.85 | | 500 | 0.06 | | 1,000 | 0.03 | | 2,000 | 0.02 | | 5,000 | 0.02 | | 8,000 | 0.01 | | 10,000 | 0.01 | **Tasks:** (a) Set up a table of intervals of random numbers ranging from 0 to 1 that can be used with the Excel VLOOKUP function to generate values for automobile collision claim payments. | Lower End of Interval | Upper End of Interval | Payment ($) | |-----------------------|-----------------------|-------------| | | | 0 | | | | 500 | | | | 1,000 | | | | 2,000 | | | | 5,000 | | | | 8,000 | | | | 10,000 | (b) Construct a simulation model to estimate the average claim payment amount (in $) and the standard deviation (in $) in the claim payment amounts. (Use at least 1,000 trials. Round your answers to two decimal places.) - **Average: $____** - **Standard Deviation: $____**
Transcribed Image Text:**Distribution of Automobile Collision Claims** An insurance company has developed the following table to describe the distribution of automobile collision claims paid during the past year. | Payment ($) | Probability | |-------------|-------------| | 0 | 0.85 | | 500 | 0.06 | | 1,000 | 0.03 | | 2,000 | 0.02 | | 5,000 | 0.02 | | 8,000 | 0.01 | | 10,000 | 0.01 | **Tasks:** (a) Set up a table of intervals of random numbers ranging from 0 to 1 that can be used with the Excel VLOOKUP function to generate values for automobile collision claim payments. | Lower End of Interval | Upper End of Interval | Payment ($) | |-----------------------|-----------------------|-------------| | | | 0 | | | | 500 | | | | 1,000 | | | | 2,000 | | | | 5,000 | | | | 8,000 | | | | 10,000 | (b) Construct a simulation model to estimate the average claim payment amount (in $) and the standard deviation (in $) in the claim payment amounts. (Use at least 1,000 trials. Round your answers to two decimal places.) - **Average: $____** - **Standard Deviation: $____**
(b) Construct a simulation model to estimate the average claim payment amount (in $) and the standard deviation (in $) in the claim payment amounts. (Use at least 1,000 trials. Round your answers to two decimal places.) average $\_\_\_\_\_$ standard deviation $\_\_\_\_\_$ (c) Let \( X \) be the discrete random variable representing the dollar value of an automobile collision claim payment. Let \( x_1, x_2, ..., x_n \) represent possible values of \( X \). Then, the mean (\( \mu \)) and standard deviation (\( \sigma \)) of \( X \) can be computed as: \[ \mu = x_1 \times P(X = x_1) + \cdots + x_n \times P(X = x_n) \] \[ \sigma = \sqrt{(x_1 - \mu)^2 \times P(X = x_1) + \cdots + (x_n - \mu)^2 \times P(X = x_n)} \] Using these formulas, calculate the mean and standard deviation (in $). (Round your standard deviation to two decimal places.) \( \mu = \$\_\_\_\_\_ \) \( \sigma = \$\_\_\_\_\_ \) Compare the values of sample mean and sample standard deviation in part (a) to the analytical calculation of the mean and standard deviation. How can we improve the accuracy of the sample estimates from the simulation? - \( \bigcirc \) We can use a different discrete distribution to generate our random variables. - \( \bigcirc \) We can decrease the number of simulation trials. - \( \bigcirc \) We can gather our data from real world samples instead. - \( \bigcirc \) We can increase the number of simulation trials. - \( \bigcirc \) We can use a different continuous distribution to generate our random variables.
Transcribed Image Text:(b) Construct a simulation model to estimate the average claim payment amount (in $) and the standard deviation (in $) in the claim payment amounts. (Use at least 1,000 trials. Round your answers to two decimal places.) average $\_\_\_\_\_$ standard deviation $\_\_\_\_\_$ (c) Let \( X \) be the discrete random variable representing the dollar value of an automobile collision claim payment. Let \( x_1, x_2, ..., x_n \) represent possible values of \( X \). Then, the mean (\( \mu \)) and standard deviation (\( \sigma \)) of \( X \) can be computed as: \[ \mu = x_1 \times P(X = x_1) + \cdots + x_n \times P(X = x_n) \] \[ \sigma = \sqrt{(x_1 - \mu)^2 \times P(X = x_1) + \cdots + (x_n - \mu)^2 \times P(X = x_n)} \] Using these formulas, calculate the mean and standard deviation (in $). (Round your standard deviation to two decimal places.) \( \mu = \$\_\_\_\_\_ \) \( \sigma = \$\_\_\_\_\_ \) Compare the values of sample mean and sample standard deviation in part (a) to the analytical calculation of the mean and standard deviation. How can we improve the accuracy of the sample estimates from the simulation? - \( \bigcirc \) We can use a different discrete distribution to generate our random variables. - \( \bigcirc \) We can decrease the number of simulation trials. - \( \bigcirc \) We can gather our data from real world samples instead. - \( \bigcirc \) We can increase the number of simulation trials. - \( \bigcirc \) We can use a different continuous distribution to generate our random variables.
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