MotoWin Auto Superstore is thinking about offering a two-year limited warranty for $952 on all new cars of a certain model. The terms of the warranty would be that MotoWin would replace the car free of charge under certain, specified conditions. Replacing the car in this way would cost MotoWin $13,600. Suppose that under the warranty, there is a 7% chance that MotoWin would have to replace the car one time and a 93% chance they wouldn't have to replace the car.If MotoWin knows that it will sell many of these warranties, should it expect to make or lose money from offering them? How much?To answer, take into account the price of the warranty and the expected value of the cost from replacing the car.MotoWin can expect to make money from offering these warranties.In the long run, they should expect to makedollars on each warranty sold.MotoWin can expect to lose money from offering these warranties.In the long run, they should expect to losedollars on each warranty sold.MotoWin should expect to neither make nor lose money from offering these warranties.

Four years ago, Victor purchased a very reliable automobile. His warranty has just expired, but the manufacturer has just offered him a 5-year, bumper-to-bumper warranty extension. The warranty costs $3,400. Victor constructs the following probability distribution with respect to anticipated costs if he chooses not to purchase the extended warranty. Cost (in $) 1,000 2,000 5,000 10,000 Probability 0.25 0.45 0.20 0.10

What type of probability distribution will most likely be used to analyse warranty repair needs on new cars in the following problem? The service manager for a new automobile dealership reviewed dealership records of the past 20 sales of new cars to determine the number of warranty repairs he will be called on to perform in the next 90 days. Corporate reports indicate that the probability any one of their new cars needs a warranty repair in the first 90 days is 0.05. The manager assumes that calls for warranty repair are independent of one another and is interested in predicting the number of warranty repairs he will be called on to perform in the next 90 days for this batch of 20 new cars sold.

Frank recently came to Canberra to study at ANU on a two-year program. He rents an apartment inGreenway and decides to buy a used car. The car costs $15000 and the seller offers an optional warranty for twoyears. With the warranty, the seller will repair (or replace) the car for free if the car fails within two years. Thewarranty costs $1800. We will try to decide if Frank should buy the extended warranty.Frank’s utility index is 𝑢(𝑥0) + 11+𝑟 𝑢(𝑥1) + 1(1+𝑟)2 𝑢(𝑥2), where 𝑥0 is his cash flow right now (either -$15000 or-$16000), 𝑥1 is his cash flow during the first year and 𝑥2 is his cash flow during the second year. Here 𝑟 = 5%. Inall cash flows, we only count the cash flows related to the possible failure of the car. Tuition, wage from part-timejobs, fuel and maintenance of the car are all ignored. The function 𝑢 has the following form:𝑢(𝑥) = 40000 ∗(1 + 𝑥20000)1∕2− 40000.To Frank’s best estimation, the car fails within one year with probability .05 and it survives the first year but failsin the second year with probability .07. If the car survives after 𝑡 years, his cash flow in year 𝑡 is zero; if the carfails in year 𝑡 with no warranty, his cash flow in year 𝑡 is -$15000, the cost of buying a replacement. For simplicity,we ignore the possibility that his replacement car, purchased in Year 1, fails in Year 2.(a) [15 marks] Determine if Frank should buy the warranty; for this part, take all the assumptions as given.(b) [5 marks] Discuss whether it is reasonable to assume that the replacement car does not fail. (Limited to 50words.)(c) [10 marks] Discuss why other cash flows such as tuition and fuel may be ignored in the analysis. (Limited to200 words.)(d) [10 marks] Consultant Bob totally disagrees with our analysis in Part (a). He argues that Frank should switchto public transportation if the car fails before he graduates. Fare is $3.2 everyday and thus about $830 ayear. Therefore, Frank’s cash flow after the failure of the car is -$830 a year without the extended warranty.Therefore, the extended warranty is a joke. Evaluate Bob’s method. (Limited to 200 words.)1

Frank recently came to Canberra to study at ANU on a two-year program. He rents an apartment inGreenway and decides to buy a used car. The car costs $15000 and the seller offers an optional warranty for twoyears. With the warranty, the seller will repair (or replace) the car for free if the car fails within two years. Thewarranty costs $1800. We will try to decide if Frank should buy the extended warranty.Frank’s utility index is 𝑢(𝑥0) + 11+𝑟 𝑢(𝑥1) + 1(1+𝑟)2 𝑢(𝑥2), where 𝑥0 is his cash flow right now (either -$15000 or-$16000), 𝑥1 is his cash flow during the first year and 𝑥2 is his cash flow during the second year. Here 𝑟 = 5%. Inall cash flows, we only count the cash flows related to the possible failure of the car. Tuition, wage from part-timejobs, fuel and maintenance of the car are all ignored. The function 𝑢 has the following form:𝑢(𝑥) = 40000 ∗(1 + 𝑥20000)1∕2− 40000.To Frank’s best estimation, the car fails within one year with probability .05 and it survives the first year but failsin the second year with probability .07. If the car survives after 𝑡 years, his cash flow in year 𝑡 is zero; if the carfails in year 𝑡 with no warranty, his cash flow in year 𝑡 is -$15000, the cost of buying a replacement. For simplicity,we ignore the possibility that his replacement car, purchased in Year 1, fails in Year 2.(a) [15 marks] Determine if Frank should buy the warranty; for this part, take all the assumptions as given.(b) [5 marks] Discuss whether it is reasonable to assume that the replacement car does not fail. (Limited to 50words.)(c) [10 marks] Discuss why other cash flows such as tuition and fuel may be ignored in the analysis. (Limited to200 words.)(d) [10 marks] Consultant Bob totally disagrees with our analysis in Part (a). He argues that Frank should switchto public transportation if the car fails before he graduates. Fare is $3.2 everyday and thus about $830 ayear. Therefore, Frank’s cash flow after the failure of the car is -$830 a year without the extended warranty.Therefore, the extended warranty is a joke. Evaluate Bob’s method. (Limited to 200 words.

Warranty records show that that the probability that a new Mercedaz car needs a repair withinthe first 90 days after delivery is 5%.Find the probability that in a random sample of six new Mercedaz cars:(i) None will require a repair within the first 90 days after delivery(ii) At most one car will require a repair within the first 90 days after delivery