The time it takes to change the oil in a car is exponentiall

The time it takes to change the oil in a car is exponentially distributed with a mean of 10 minutes. What is the probability that it will take a mechanic less than 6 minutes to change the oil? What is the probability that it will take a mechanic between 3 and 5 minutes to change the oil?

Solution

A)

The left tailed area in an exponential distribution is          

Area = 1 - e^(-lambda*x)          
          
As          
          
x = critical value =    6      
          
          
Then          
          
Area =    0.451188364   [answer]

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b)

          
The area between two values in an exponential distribution ois          
          
Area = e^(-lambda*x2) - e^(-lambda*x1)          
          
As          
          
x1 = lower bound =   3      
x2 = upper bound =    5      
          
Then          
          
Area =    0.134287561   [ANSWER]