Question

CD player warranty :replacement time for CD players that fail are randomly distributed with a mean of 7.1 years and standard deviation of 1.4 year ( bases on data from"getting thing fixed " consumer reports)

a- find the probability that a randomly selected CD player will have a replacement time less than 8.0 years

b- if you want to provide a warranty so that only 2% the CD players will fail before the warranty expires , what the time length of warranty ?

Answer 1

Given mean=7.1, s=1.4

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(a) P(X<8) = P((X-μ)/s <(8-7.1)/1.4)

=P(Z< 0.64)

=0.7389 (check standard normal table)

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(b) P(X<c) = 0.02

--> P(Z<(c-7.1)/1.4) = 0.02

--> (c-7.1)/1.4 =-2.05(check standard normal table)

--> c = 7.1 -2.05*1.4 =4.23