The following table provides the expected repair cost of a laptop and respective

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

What is the probability of any failure that require repair in the next 5 years?

What is the expected repair cost? What is the Standard deviation of repair cost? Hint: Use Excel.

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?

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

1)probability of any failure that require repair in the next 5 years =P(Minor)+P(Major)+P(Catastrophic)=0.13+0.08+0.04

=0.25

2)

from above  expected repair cost =73

standard deviation =168.43

c) expected gain or loss =expected repair cost -premium =73-99=$-26

as ths policy have expected loss of $ 26 threfore we should not recommend to purchase this warranty

d)

as $59.95 cost is less than expected repair cost ; therefore one should purchase this warranty.

repair cost(y) p(y) yP(y) y2P(y) (y-)2 (y-)2P(y) None 0 0.750 0.000 0.000 5329.000 3996.750 Minor 100 0.130 13.000 1300.000 729.000 94.770 Major 400 0.080 32.000 12800.000 106929.000 8554.320 Catastrophic 700 0.040 28.000 19600.000 393129.000 15725.160 total 1 = 73.00 33700.000 506116.000 2= 28371.0000 std deviation=     =    2 = 168.4369

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