You buy a cell phone for $100 and there is a 8% chance that it will fail. You ca
ID: 3044456 • Letter: Y
Question
You buy a cell phone for $100 and there is a 8% chance that it will fail. You can pay an additional $6 for the hassle-free replacement warranty. This means if it fails you will get a free replacement.
(a) Suppose you do not buy the warranty but will buy a second one if the first one fails (we will assume this second one does not fail) and you will pay the full $100 for the second one. Complete the following table to assist in calculating the expected cost for this phone. Enter the probabilities to 2 decimal places.
(b) Use the table to calculate the expected value for the cost of this phone. Round your answer to the nearest penny.
$
(c) Considering the expected cost above and the price of the warranty ($6), did you make the right decision to not buy the warranty and why? There is only one correct answer and explanation.
Yes, because the expected cost is less than the cost of the phone plus the warranty.
No, because the expected cost is greater than the cost of the phone plus the warranty.
Yes, because the expected cost is greater than the cost of the phone plus the warranty.
No, because the expected cost is less than the cost of the phone plus the warranty.
Outcomes cost = x Probability = P(x) It fails It doesn't failExplanation / Answer
a) The following table completed:
b) With the help of the table above,
Expected value of X = E(X) = X1P(X1) + X2P(X2)
E(X) = 200(0.08) + 100(0.92)
E(X) = 16 + 92 = 108
Therefore, the expected cost of the phone is $108.
Ans: $108
c) Okay, so there are two cases:
i) Don't buy the warranty and expected cost of phone = $108
ii) Buy the warranty and expected cost of phone = $106 (Because even if the phone fails, you get the 2nd one for free, so you pay $106 even if the phone fails or doesn't fail)
Hence, we see that buying the warranty would be a better choice as the expected cost of the phone is lesser then.
Ans: B) No, because the expected cost is greater than the cost of the phone plus the warranty.
Cheers!
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Outcomes Cost = X Probability = P(X) It fails 200 0.08 It doesn't fail 100 0.92Related Questions
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