Question

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A new car battery is sold with a two-year warranty whereby the owner gets the battery replaced free of cost if it breaks down during the warranty period. Suppose an auto store makes a net profit of $20 on batteries that stay trouble-free during the warranty period; it makes a net loss of $10 on batteries that break down. The life of batteries is known to be normally distributed with a mean and a standard deviation of 40 and 16 months, respectively.


a. What is the probability that a battery will break down during the warranty period? Use either the pnorm or qnorm R command to determine the answer. (Round your answer to 4 decimal places.)



b. What is the expected profit of the auto store on a battery? (Round your answer to 3 decimal places.)



c. What is the expected monthly profit on batteries if the auto store sells an average of 500 batteries a month? (Round your answer to 2 decimal places.)

d. What should be the warranty period (in months) if the manufacturer wants no more than 5% of batteries to break down during the warranty period? Use either the pnorm or qnorm R command to determine the answer. (Round your answer to 1 decimal place.)

Answer 1

R commands for a) part

pnorm(24,40,16)
[1] 0.1586553

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