Question

f(t) = A manufacturer guarantees a product for 1 year. The lifespan of the product after it is sold is given by the probability density function below, where t is time in months. 0.01e-0.011t ift20 otherwise What is the probability that a buyer chosen at random will have a product failure (A) During the warranty? (B) During the second year after purchase? (A) What is the probability that the product will fail within one year? (Round to three decimal places as needed.) (B) What is the probability that the product will fail during the second year after purchase? (Round to three decimal places as needed.)

Answer 1

@ The warranty period is te [9,12] Hence, the probability that the buyer, chosen randomly, have will have Product failure in this period dt. 12 12 s f(t) at 0.0ll.e-0.01€ 0 12 12 0.01. -0.01t е. -0.01 O Second 24 0.01 dit : 0.011 * 100 * (1-2-0.12). = 1-1 (1-2-0-2) = 0.1243815 Copprox). (③) Similarly the probability of failure in the year after purchase e-0.01t 6-os e-024). lol x 0.1002925757 ~ 0.1103218332 (approxoa) S 24 0.011. e-0.01€ = 1:1 x -0.01 12 Scanned with CamScanner

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