Problem 2: Cost of Refrigerator Warranty: August 2017 issue of Consumer Reports

Question

Problem 2: Cost of Refrigerator Warranty: August 2017 issue of Consumer Reports indicated that the average life of a LG refrigerator before replacement is given by mean, 13.5 years and standard deviation 2.25 years. Let x be equal to the age at which the refrigerator is replaced. Assume that x has an approximately normal distribution. a) What is the probability that a typical buyer will keep a refrigerator fewer than 11.5 years more than 17.5 years before replacement?before replacement? b) What is the probability that a typical buyer will keep a refrigeratoir c) Inverse Normal Distribution: Suppose the company guarantees its refrigerators for parts and labor and will replace a refrigerator that breaks during the maximum warranty period, with a new one that cost same as the original one. However, the company does not want to replace more than 5% of the refrigerators under guarantee. What should be the maximum warranty period in years that the company should advertise for its refrigerator so that it doesn't lose money? Express the answer to the nearest tenth of a year.

Explanation / Answer

mean = 13.5 , s = 2.25
a)
P(x < 11.5)
z = ( x - mean) / s
= ( 11.5 - 13.5) / 2.25
= -0.8889
P(x < 11.5)= P(z < -0.8889) = 0.1870

b)
P(x > 17.5)
z = ( x - mean) / s
= ( 17.5 - 13.5) / 2.25
= 1.7778
P(x > 17.5)= P(z >1.7778 ) = 0.0377

c)
z valie at 5% = 1.645
z = (x -mean) / s
1.645 = ( x - 13.5) / 2.25
x = 17.2013

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