An automobile insurance company issues a one-year policy with a deductible of 500. The probability is 0.8 that the insured automobile has no accident and 0.0 that the automobile has more than one accident. If there is an accident, the loss before application of the deductible is exponentially distributed with mean 3000. Calculate the 95th percentile of the insurance company payout on this policy.

y₀.₉₅ = 3659

Step-by-step explanation:

P( no accident ) = 0.8

P( one accident ) = 0

deductible = 500

mean = 3000

Determine the 95th percentile of the insurance company payout

Assuming : y =company payout , x =amount of loss incurred due to accident

Then :

P( x < 500 ) = 0.2 ( 1 - e^-500/3000)

                   = 0.2 ( 1 - e^-1/6 )

95th percentile =

= P( y < y₀.₉₅  ) 0.95

  P( y = 0 ) = 0.8 + 0.2 ( 1 - e^-1/6 ) = 0.8307

attached below is the remainder of the solution

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