Question

A life insurance company has determined that each week an average of seven claims is filed in its Nashville branch.

a. What is the probability that during the next week exactly seven claims will be filed?
b. What is the probability that during the next week no claims will be filed?
c. What is the probability that during the next week fewer than four claims will be filed?
d. What is the probability that during the next week at least seventeen claims will be filed?

Answer 1

Given:
A life insurance company has determined that each week an average of seven claims is filed in its Nashville branch

It follows poison distribution with mean (λ) = 7

Probability function of poison distribution = (e^-λ λ^x)/x!

probability that during the next week exactly seven claims will be filed is P(x=7) = (e^-7 7⁷)/7! = 0.149

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probability that during the next week no claims will be filed is P(x=0) = 0.0009

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probability that during the next week fewer than four claims will be filed is P(x<4) =0.0817

probability that during the next week at least seventeen claims will be filed is P(X>=17)= 1-P(x<=16) = 1-0.999

= 0.001

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