2. The normal distribution Aa Aa An automobile battery manufacturer offers a 31/

Question

2. The normal distribution Aa Aa An automobile battery manufacturer offers a 31/54 warranty on its batteries. The first number in the warranty code is the free-replacement period; the second number is the prorated credit period. Under this warranty, if a battery fails within 31 months of purchase, the manufacturer replaces the battery at no charge to the consumer. If the battery fails after 31 months but within 54 months, the manufacturer provides a prorated credit toward the purchase of a new battery. The manufacturer assumes that x, the lifetime of its auto batteries, is normally distributed with a mean of 45 months and a standard deviation of 5.6 months. Use the following Distributions tool to help you answer the questions that follow. (Hint: When you adjust the parameters of a distribution, you must reposition the vertical line (or lines) for the correct areas to be displayed.) Select a Distribution Distributions of its batteries free of charge. If the manufacturer's assumptions are correct, it would need to replace

Explanation / Answer

1)ashe would have to chage the bttery if it fails with in 31 months

hence P(X<30) =P(Z<(31-45)/5.6)=P(Z<-2.5)=0.0062 or 0.62% of batteries free of charge

2)for 1.07% , z=-2.30085

hence std deviation=(31-45)/(-2.30085)=6.0847

3)for P(31<X<54)=P(-2.30085<Z<1.4791)=0.9304-0.01 =0.9199 or 91.99%

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