An insurance policy costs S100 and will pay policyholders $8,000 if they suffer

Question

An insurance policy costs S100 and will pay policyholders $8,000 if they suffer a major injury (resulting in hospitalization) or $2500 if they suffer a minor injury (resulting in lost time from work). The company estimates that 1 in every 1936 policyholders will suffer a major injury and that 1 in 514 will suffer a minor injury. a) Create a probability model for the profit on a policy. b) What's the company's expected profit on the policy? c) What's the standard deviation? a) First find the probability and profit for each outcome P(event) Profit no injury major injury minor injury (Round to six decimal places as needed.) b) Find the expected profit on the policy EX)-S (Round to two decimal places as needed.) c) Find the standard deviation on the policy. SD(X)-$ (Round to two decimal places as needed.)

Explanation / Answer

here for major injury ; profit =100-8000=-7900 and probability =1/1936=0.000517

for minor injury ; profit =100-2500=-2400 and probability =1/514=0.001946

for no injury ; profit =100=100 and probability =1-0.000517-0.001946=0.997538

from above

b)

for above model:

E(X)=91.00

=212.45

x P(event) profit no injury 0.997538 100 major injury 0.000517 -7900 minor injury 0.001946 -2400

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