An insurance company issues 1250 vision care insurance policies. The number of claims filed by a policyholder under a vision care insurance policy during one year is a Poisson random variable with mean 2. Assume the numbers of claims filed by different policyholders are mutually independent.

Calculate the approximate probability that there is a total of between 2450 and 2600 claims during a one-year period?

• 0.68
• 0.82
• 0.87
• 0.95
• 1.00

Copyright 2023. The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.

Solution: E

The tour operator collects 21 x 50 = 1050 for the 21 tickets sold. The probability that all 21 passengers will show up is

(1 − 0.02 )21  = (0.98)21 = 0.65. 

Therefore, the tour operator’s expected revenue is

1050 – 100(065) = 985.

Copyright 2023. The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.