The time it takes a mechanic to change the oil in car isexponentially distribute

Question

The time it takes a mechanic to change the oil in car isexponentially distributed with a mean of 5 minutes. a. What is the probability that it will take a mechanic lessthan 6 minutes to change the oil? b. What is the probability that it will take a mechanicbetween 3 and 5 minutes to change the oil? ANS: a. 0.6988 b. 0.1809 The time it takes a mechanic to change the oil in car isexponentially distributed with a mean of 5 minutes. a. What is the probability that it will take a mechanic lessthan 6 minutes to change the oil? b. What is the probability that it will take a mechanicbetween 3 and 5 minutes to change the oil? ANS: a. 0.6988 b. 0.1809

Explanation / Answer

Let X be the time it takes for the mechanic to change the oil inthe car. Then X has an exponential distribution with parameter; X~Exp(=1/ = 1/5 = 0.2). a.) P(X < 6) = 1 - P(X > 6) = 1 - e-x = 1 -e-(0.2)(6) = 1 - 0.3011942 = 0.6988059 b.) P(3

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