A particular insurance company pays out an average of4 major medical claims in a

Question

A particular insurance company pays out an average of4 major medical claims in a month. Using the Poisson distribution approximate 1. the probability that it pays no major medical claims in the coming month? 2. the probability that it pays at most 2 major medical claims in the coming month? 3. the probability that it pays at least 4 major medical claims in the coming month? The records of an Italian shoe manufacturer show that 10% of shoes made are defective. Assuming independence, find the probability of getting: 1. defective shoes in a batch of 12. 2. 6 defective shoes in a batch of 20.

Explanation / Answer

average of no of medical claims in a month i.e = 4

P(X=n) = e-n/n!

1)

probability that if pays no major medical claims in the coming month i.e P(X=0)

P(X=0) = e-440/0! = 0.0183

2)

probability that atmost 2 major medical claims in the coming month i.e P(X<=2)

P(X<=2) = P(X=0)+P(X=1)+P(X=2)

= e-440/0! +e-441/1!+e-442/2!  

= 0.2381

3)

probability that it pays atleast 4 major medical claims in the coming month i.e P(X>=4)

P(X>=4) = 1-P(X=0)-P(X=1)-P(X=2)-P(X=3)

= 1- e-440/0! -e-441/1!-e-442/2! -e-443/3!

= 0.5665

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