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Need help with part d). Thank you :)

Need help with part d). Thank you :)

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter13: Probability And Calculus
Section13.2: Expected Value And Variance Of Continuous Random Variables
Problem 10E
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Need help with part d). Thank you :)

 

Based on claims records kept over a long period, an insurance company estimates the probability distribution of the number of claims a randomly selected policyholder will make in five years. Call this random variable X. The estimated distribution of X is shown in the table at the top of the next page. X 0 1 2 3 4 5 6 P(X=x) 0.317 0.286 0.199 0.121 0.056 0.014 0.007 a) Calculate the mean and variance of X. b) Calculate the mean and variance of the total number of claims that would be made by 1000 policyholders in five years. c) State the approximate distribution of the total number of claims made by 1000 policyholders in five years. On what theoretical basis can this approximation be made? d) What are the approximate probabilities 1000 policyholders will make: i. more than 1400 claims in five years. 11. between 800 and 1500 claims in five years.
Transcribed Image Text:Based on claims records kept over a long period, an insurance company estimates the probability distribution of the number of claims a randomly selected policyholder will make in five years. Call this random variable X. The estimated distribution of X is shown in the table at the top of the next page. X 0 1 2 3 4 5 6 P(X=x) 0.317 0.286 0.199 0.121 0.056 0.014 0.007 a) Calculate the mean and variance of X. b) Calculate the mean and variance of the total number of claims that would be made by 1000 policyholders in five years. c) State the approximate distribution of the total number of claims made by 1000 policyholders in five years. On what theoretical basis can this approximation be made? d) What are the approximate probabilities 1000 policyholders will make: i. more than 1400 claims in five years. 11. between 800 and 1500 claims in five years.
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