Statistics Help

Question

An LG Dishwasher, which costs $750, has a 15% chance of needing to be replaced in the first 2 years of purchase. A two-year extended warrantee costs $112.10 on a dishwasher. Assume the dishwasher is replaced in the first 2 years.

a) Write out the probability distribution for the value of the extended warranty.

   Make sure you enter your X values from smallest to largest.

X	P(X)

b) What is the expected value of the extended warranty?

  Round final answer to 2 decimal places and write the units in the second box.

Answer 1

Hi Gianna,

a. Think about the cost-benefit analysis when evaluating warranties. If the dishwasher breaks within two years, the corresponding x-value will be (750 - 112.10) = $637.90. You need to subtract the amount you paid for the warranty from the cost of the dishwasher. Now, the probability of that happening is 15% or 0.15. So first entry in your table should be:

X P(X=x)

$637.90 0.15

Now, it's also possible that you purchase the warranty and nothing goes wrong. Use the Complement Rule here--the probability that the dishwasher lasts more than two years is 1 - 0.15 = 0.85. This corresponds to an outright loss of your warranty price, $112.10, which corresponds to an x-value of - $112.10. So, to fill out the table:

X P(X=x)

$637.90 0.15

$-112.10 0.85

b) Formula for Expected Value:

E(x) = Sum[x*P(x)]

Thus:

E(x) = (637.90*0.15) + (-112.10*0.85)

E(x) = 0.40

So the expected value is about 40 cents. It's a judgment call on whether or not that warranty is worth buying. While you do stand to gain, i.e. positive expected value, it isn't by much. I hope this helps.