The time it takes a mechanic to change the oil in a car is exponentially distributed with a mean of 5 minutes. What is the probability that it will take a mechanic up to 6 minutes to change the oil?
Let X be the time it takes for the mechanic to change the oil inthe car. Then X has an exponential distribution with parameterλ; X~Exp(λ=1/μ = 1/5 = 0.2).
P(X < 6) = 1 - P(X > 6) = 1 - e-λx = 1 -e-(0.2)(6) = 1 - 0.3011942 = 0.699
The time it takes a mechanic to change the oil in a car is exponentially distributed...
The time taken by an auto mechanic to complete an oil change is random with mean 30.5 minutes and standard deviation of 2 minutes. a) What is the probability that 40 oil changes take more than 1250 minutes? b) What is the probability that a mechanic can complete 60 or more changes in less than 1850 minutes?
Two turtles are racing. The length of time that turtle A takes is expo 2 exponentially distributed with mean 5 minutes. The length that turtle B take is also exponentially distributed but with mean 7 minutes. Assume tha their times are independent. (a) What is the probability that A wins? (b) What is the probability that the winner takes longer than 6 minutes (c) What is the expected time of the winner? (d) What is the probability of a tie?
4. The time (in minutes) that it takes a mechanic to change oil has an exponential distribution with mean 25 a) Find PX22), P(X> 15), and P(15 <X<22) b) Find the median.
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12. The time it takes a mechanic to change oil has an exponential distribution with mean 20· +' a) Set up an integral to find P(15 < X < 25), then evaluate the integral.+ 4 b) Find the 40th percentile
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Q7.The time it takes a worker on an assembly line to complete a task is exponentially distributed with a mean of 10 minutes. a. What is the probability that it will take a worker less than 8 minutes to complete the task? b.What is the probability that it will take a worker between 8 and 12 minutes to complete the task?
8. Assume that the length of time needed to change the oil in a car at Fiona's Service Station is normally distributed with mean u = 15 minutes, and a standard deviation o = 5 minutes. If Fiona decides to offer a discount to those customers whose cars take the longest 20% of servicing time, what is the cutoff for the time required to receive the discount? EXCEL COMMAND
The time that it takes for a mechanic to fix a car has a uniform distribution from 4 to 9 days. Find the probability that it takes the mechanic 6 or more days to fix the car.
3. Two turtles are racing. The length of time that turtle A takes is expo 2 nentially distributed with mean 5 minutes. The length that turtle B take is also exponentially distributed but with mean 7 minutes. Assume tha their times are independent. (a) What is the probability that A wins? (b) What is the probability that the winner takes longer than 6 minutes (c) What is the expected time of the winner? (d) What is the probability of a...
The owner of an oil change shop would like to know the mean time it takes to do an oil change at the shop. He takes a random sample of 16 cars that are serviced and finds a sample average of 20.5 minutes and a standard deviation of 7.4 minutes Construct a 90% confidence interval for the true mean time to do an oil change to a car. a) Lower Bound b) Upper Bound