Question

The number of insurance claims in a given period is a Poisson random variable. The policies at a certain car insurance company cover expenses up to a maximum of $100 000. In this company, they observe that each claim they receive is, in average, for a value of $10 000, with standard deviation of $1000. In a month, they receive in average 35 claims.

Is it likely that they will have to reimburse more than $385 000 in March 2019?

Answer 1

for normal distribution z score =(X-μ)/σ
here mean=       μ=	10000
std deviation   =σ=	1000.0000
sample size       =n=	35
std error=σx̅=σ/√n=	169.0309

P( reimburse more than $385 000 ) =P(reimburse on average 385000/35 =110000 per person)

probability =

P(Xbar>11000)

=

P(Z>5.92)=

1-P(Z<5.92)=

1-1=

0.0000

therefore it is not likely that t they will have to reimburse more than $385 000 as the probability of above event is almost negligible,