SOLUTION: Please help me.....I am having a hard time solving this problem. The operating life of a Sports Master fishing reel is normally distributed with mean 48 months and standard devi

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Question 438334: Please help me.....I am having a hard time solving this problem.
The operating life of a Sports Master fishing reel is normally distributed with mean 48 months and standard deviation 6 months. The manufacturer will replace any Sports Master reel that malfunctions during the guarantee period.
a) if the guarantee period is 45 months, what percent of the reels will Sports Master have to replace? compute.
b) How long should the guarantee period be if the manufacturer does not want to replace more than 5% of the reels?
Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
The operating life of a Sports Master fishing reel is normally distributed with mean 48 months and standard deviation 6 months. The manufacturer will replace any Sports Master reel that malfunctions during the guarantee period.
a) if the guarantee period is 45 months, what percent of the reels will Sports Master have to replace? compute.
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z(45) = (45-48)/6 = -1/2
% of sales covered by the warranty = P(z < -1/2) = 0.3085 = 30.85%
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b) How long should the guarantee period be if the manufacturer does not want to replace more than 5% of the reels?
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Find the z-value with a left tail of 5%
invNorm(0.05) = -1.645
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Find the corresponding x-value:
x = zs+u
x = -1.645*6+48 = 38.13 months
Make the guarantee period 39 months
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Cheers,
Stan H.