The Time It Takes a Mechanic to Change the Oil

question 51

Essay

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

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Definitions:

Random Sample

A subset of individuals chosen from a larger set where each individual has an equal chance of being selected, designed to represent the larger group.

Waiting Time

The period between a request or need for service and the actual provision of that service, often analyzed in queue theory and service operations.

Standard Deviation

Standard deviation is a measure of the amount of variation or dispersion of a set of values, indicating how much the values in a data set differ from the mean.

Confidence Interval

A range of values, derived from sample statistics, that is believed to contain the value of an unknown population parameter with a certain probability.