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 10 months, respectively.

a. What is the probability that a battery will break down during the warranty period?

b. What is the expected profit of the auto store on a battery?

c. What is the expected monthly profit on batteries if the auto store sells an average of 500 batteries a month

Answer 1

Answer:

Given that:

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 10 months, respectively.

a)  What is the probability that a battery will break down during the warranty period?

Find the probability that a battery will break down during the warranty period

It is given that, a car battery has two-year warranty (=24 months)

The life of batteries is to be normally distributed with a mean of 40 months and standard deviation of 10 months

That is, and  

If a battery breaks down during the warranty period, it makes a net loss of $10 on a battery

If a battery breaks down after the warranty period, it makes a net profit of $20 on a battery.

The probability that a battery will break down during the warranty period is

The required probability is

The probability is 0.0548

Thus the probability that a battery will break down during the warranty period is 0.0548

That is,if a battery will break down during the warranty period then the loss for an auto store is $0.0548

b) What is the expected profit of the auto store on a battery?

Find the expected profit of the auto store on a battery

If a battery will break down after the warranty period then there will be profit for an auto store

The probability that a battery will break down after the warranty period is

The required probability is

The probability is 0.9452

The required expected profit is

c)  What is the expected monthly profit on batteries if the auto store sells an average of 500 batteries a month

Find the expected monthly profit on batteries if the auto store sells an average of 50 batteries a month

Suppose X be the monthly profit on a battery is $ 18.356

The expected monthly profit on batteries if the auto store sells an average of 500 batteries a month is

Thus,the expected monthly profit on batteries if the auto store sells an average of 500 batteries a month is $9,178