Question 4

a. A company establishes a fund of 120 from which it wants to pay an amount, C, to any of its 20 employees who achieve a high-performance level during the coming year. Each employee has a 5% chance of achieving a high-performance level during the coming year. The events of different employees achieving a high-performance level during the coming year are mutually independent. Calculate the maximum value of C for which the probability is less than 1% that the fund will be inadequate to cover all payments for high-performance. (10 marks).

b. The lifetime of a printer costing 200 is exponentially distributed with mean 2.5 years. The manufacturer agrees to pay a full refund to a buyer if the printer fails during the first year following its purchase, a one-half refund if it fails during the second year, and no refund for failure after the second year. Calculate the expected total amount of refunds from the sale of 150 printers. (15 marks)