1.An insurance policy is written to cover a loss, X, where XX has a uniform dist

Question

1.An insurance policy is written to cover a loss, X, where XX has a uniform distribution on [0,2000]. The policy has a deductible, d, and the expected payment under the policy is 25 of what it would be with no deductible. Calculate d.

2.The annual profit of a life insurance company is normally distributed.
The probability that the annual profit does not exceed 1500 is 0.7596. The probability that the annual profit does not exceed 2500 is 0.7967.
Calculate the probability that the annual profit does not exceed 1000.

Explanation / Answer

Expected payment = Mean of Uniform distribution = (0+2000)/2 =1000

1000 = 25d

or d = 40

2) P(Profit > 1500 ) = 0.7596

Putting in formula for normal distribution

(1500-x)/ sigma = Norm^-1 ( 0.7596) = 0.705016

(2500-x)/sigma = Norm^-1 ( 0.7967)= 0.829892

Sigma = 8007,

x= -4144

z= 1000- (-4144) / 8007 = 0.6424

P(x) = 0.7396

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