The following table provides the expected repair cost of a laptop and respective
ID: 3045727 • Letter: T
Question
The following table provides the expected repair cost of a laptop and respective probabilities (likelihood) for 5 years after purchase.
Type of Repair
Probability
Repair Cost
None
0.75
$0
Minor
0.13
$100
Major
0.08
$400
Catastrophic
.04
$700
a. What is the probability of any failure that require repair in the next 5 years?
b. What is the expected repair cost? What is the Standard deviation of repair cost? Hint: Use Excel.
c. If the cost of purchasing a 5-year warranty is $99, calculate the expected gain or loss for a consumer that purchase this warranty. Would you recommend purchasing a warranty? Why?
d. Would you a buy 5-year warranty if it costs $59.95?
Type of Repair
Probability
Repair Cost
None
0.75
$0
Minor
0.13
$100
Major
0.08
$400
Catastrophic
.04
$700
Explanation / Answer
a) Probability = 1-0.75=0.25
b)Expected repair cost=0.13*100+0.08*400+0.04*700=13+32+28=73
SD=[ 0.75*[0-73]^2+0.13*27^2+0.08*377^2+0.04*677^2 ]^0.5=183.83
c) Expected loss from warranty purchase= 99-73=26. No, we would not recommend .
d( If cost is 59.95, net gain = 73-59.95=13.05 which is positive. Hence, we should buy it.
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