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In: Statistics and Probability

An insurance company insures 2,000 people each year, each of whom has a 1/1000 chance of...

An insurance company insures 2,000 people each year, each of whom has a 1/1000 chance of an accident in 1 year. Use the Poisson approximation to compute the probability that there will be at most 2 accidents. Also, calculate the exact binomial-(n,p) probability

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Expert Solution

Ans:

Given that

n=2000

p=1/000

Poisson approximation:

mean=np=2000*(1/000)=2

P(x=k)=exp(-2)*(2^k/k!)

P(at most 2)=P(x<=2)

=P(x=0)+P(x=1)+P(x=2)

=exp(-2)*(2^0/0!+2^1/1!+2^2/2!)=0.6767

orchestra answered 2 years ago
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