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 16,000 hours of operation. On average, the wash-down motors operate for 18,000 hours with a standard deviation of 1,450 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 20,900 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 failure have to be if the standard deviation remains at 1,450 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.)

b. It can be expected that _______% of wash-down motors will operate for more than 20,900 hours. (Round to two decimal places as needed.)

c. The average hours of operation before failure would have to be _________ hours.

Explanation / Answer

a)

P(X <16000) = P(Z < 16000-18000/1450)

= P(Z < -1.3793)

=

b)

P(X > 20900) = P(Z > 20900 - 18000/1450)

= P(Z > 2)

c)

P(X < 16000) = 1%

=>

16000- x/1450 = invnorm(0.01) = -2.326

=>

average hours of operation x = 19372.7

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

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