Question

Four years ago, Victor purchased a very reliable automobile. His warranty has just expired, but the manufacturer has just offered him a 5-year, bumper-to-bumper warranty extension. The warranty costs $3,400. Victor constructs the following probability distribution with respect to anticipated costs if he chooses not to purchase the extended warranty 900 2,800 4,700 11,000 0.19 0.48 0.20 0.13 a. Calculate Victor's expected cost Expected cost b. Given your answer in part a, should Victor purchase the extended warranty? (Assume risk neutrality.) ONo, because his expected cost without the extended warranty is less than the cost of the warranty O Yes, because his expected cost without the extended warranty is greater than the cost of the warranty

Answer 1

a.
Victor expected cost = $\sum_i Probability_i * Cost_i$

= 0.19 * 900 + 0.48 * 2800 + 0.20 * 4700 + 0.13 * 11000

= 3885

b.

As, the expected cost of $3885 is greater than the warranty costs $3400, Victor should by the warranty to minimize its cost.

The answer is,

Yes, because his expected cost without the extended warranty is greater than the cost of the warranty.