Question 933930: 11. An automobile battery manufacture offers an 18 month warranty on its car batteries. Under this warranty, if a battery fails within 18 months of purchase, the manufacturer replaces the battery at no charge to the consumer. Assume that the lifetime of its car batteries is normally distributed with a mean of 32 months and a standard deviation of 7 months.
A. What percentage of batteries will be replaced free of charge?
B. If 200 batteries are sold in a given year each costing $150.00, then what was the total warranty costs of replacing defective batteries free ( Round up if necessary)
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! An automobile battery manufacture offers an 18 month warranty on its car batteries. Under this warranty, if a battery fails within 18 months of purchase, the manufacturer replaces the battery at no charge to the consumer. Assume that the lifetime of its car batteries is normally distributed with a mean of 32 months and a standard deviation of 7 months.
A. What percentage of batteries will be replaced free of charge?
z(18) = (18-32)/7 = -2
P(x < 18 months) = P(z < -2) = 0.02275 = 2.275% will fail in less than 18 months
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B. If 200 batteries are sold in a given year each costing $150.00, then what was the total warranty costs of replacing defective batteries free ( Round up if necessary)
Ans: 150*0.02275*200 = $682.50
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Cheers,
Stan H.
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