An extended warranty is a prolonged warranty offered to consumers by the warranty administrator, the retailer, or the manufacturer. A recent report in The New York Times (November 23, 2009) suggests that 20.4% of laptops fail over three years. Roberto D’Angelo is interested in an extended warranty for his laptop. A good extended warranty is being offered at Compuvest.com for $74. It will cover any repair job that his laptop may need in the next three years. Based on his research, he determines that the likelihood of a repair job in the next three years is 13% for a minor repair, 8% for a major repair, and 3% for a catastrophic repair. The extended warranty will him $80 for a minor repair, $320 for a major repair, and $500 for a catastrophic repair. These results are summarized in the following probability distribution.
Type of Repair
Probability
Repair Cost
None
0.76
$0
Minor
0.13
$80
Major
0.08
$320
Catastrophic
0.03
$500
In a report, use the above information to:
1. Calculate and interpret the expected value of the repair cost.
2. Analyze the expected gain of loss for a consumer who buys the above extended warranty.
3. Determine what kind of a consumer (risk neutral, risk averse, or both) will buy this extended warranty.
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