The normal distribution An automobile battery manufacturer offers a 22/37 warran

Question

The normal distribution An automobile battery manufacturer offers a 22/37 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 falls within 22 months of purchase, the manufacturer replaces the battery at no charge to the consumer. If the battery falls after 22 months but within 37 months, the manufacturer provides 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 30 months and a standard deviation of 3.5 months. Use the following Distributions tool to help you answer the questions that follow. If the manufacturer's assumptions are correct, R would need to replace of its batteries free of charge. The company finds that it is replacing 1.54% of its batteries free of charge. It suspects that its assumption about the standard deviation of the life of its batteries is incorrect. A standard deviation of results in a 1.54 % replacement rate. Using the revised standard deviation for battery life, what percentage of the manufacturer's batteries don't quality for free replacement but do quality for the prorated credit? 2.49% 95.52% 47.06% 48.46%

Explanation / Answer

from normal distribution Z =(X-mean)/std deviation

mean =30 months and std deviation =3.5 months

for replacement P(X<22) =P(Z<(22-30)/3.5) =P(Z<-2.2857) =0.0114

hence he needs to replace 1.114% of its battery free of charge

at 1.54% ; z=-2.1596

hence std deviation =(X-mean)/z =(22-30)/-2.1596 =3.70 result in a 1.54%

P(22<X<37) =P((22-30)/3.70<Z<(37-30)/3.70) =P(-2.1596<Z<1.8897) =0.9706-0.0154 =0.9552

hence option 95.52% is correct

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.