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29 October, 08:57

An auto insurance company is implementing a new bonus system. In each month, if a policyholder does not have an accident, they will receive a cash-back bonus of 5 from the company. Among the 1000 policyholder of the auto insurance company, 400 are classified as low-risk drivers and 600 are classified as high-risk drivers. In each month, the probability of zero accidents for high-risk drivers is 0.80 and the probability of zero accidents for low-risk drivers is 0.90. Calculate the expected bonus payment from the company to the 1000 policyholders in one year.

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  1. 29 October, 10:09
    0
    50,400

    Explanation:

    Using application of total expectation, E;

    N = Number of policy holders who have zero accidents in one month

    P = Probability

    N|Low = 400

    N|High=600

    P|Low=0.9

    P|High=0.8

    Therefore E = (N|Low*P|Low) + (N|High*P|High)

    E = (400*0.9) + (600*0.8)

    E=360+480

    E=840

    Then Total bonus for the year B

    B = E*12*5

    B=840*12*5

    B=50,400
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