A company manufactures a wash-down motor that is used in the food processing ind

Question

A company manufactures a wash-down motor that is used in the food processing industry. The motor is marketed with a warranty that guarantees it will be replaced free of charge if it fails within the first 14,000 hours of operation. On average, the wash-down motors operate for 18,000 hours with a standard deviation of 3,650 hours before failing. The number of operating hours before failure is approximately normally distributed a. What is the probability that a wash-down motor will have to be replaced free of charge? b. What percentage of wash-down motors can be expected to operate for more than 25,300 hours? C. If the company wants to design a wash-down motor so that no more than 1% are replaced free of charge, what would the average hours of operation before fa re have to be if the standard deviation remains at 3,650 hours? a. The probability that a wash-down motor will have to be replaced free of charge is (Round to four decimal places as needed.)

Explanation / Answer

Ans:

Given that

mean=18000

standard deviation=3650

a)

z(14000)=(14000-18000)/3650=-1.096

P(x<14000)=P(z<-1.096)=0.1366

b)

z(25300)=(25300-18000)/3650=2

P(z>2)=1-P(z<2)=1-0.9772=0.0228

c)P(Z<=z)=0.01

z=-2.33

-2.33=(14000-mean)/3650

mean=14000+2.33*3650=22504.5 hrs

(note:if z value is not rounded off ,then mean=22491.17 hrs)

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