A new car battery is sold with a two-year warranty whereby the owner gets the ba

Question

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? (Round your answer to 4 decimal places.) Probability

b. What is the expected profit of the auto store on a battery? (Do not round intermediate calculations. Round your answer to 3 decimal places.) Expected profit $

c. What is the expected monthly profit on batteries if the auto store sells an average of 500 batteries a month? (Do not round intermediate calculations. Round your answer to 2 decimal places.) Expected monthly profit $

Explanation / Answer

here warranty period =2 years =2*12 =24 months

a) probability that a battery will break down during the warranty period=P(X<24) =P(Z<(24-40)/16)=P(Z<-1)

=0.1587

b) expected profit =expected gain -expected claim =(1-0.1587)*20-0.1587*10=15.239 (~15.240)

c) expected monthly profit =500*15.239 =7619.50 ( 7620.17)

(Note: exact answer without rounding is in bracket)

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