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Assume that an engine service is made up of a large number, n, of individual tasks,...

Assume that an engine service is made up of a large number, n, of individual tasks, and the time to complete each task follows an exponential distribution with mean M hours. Also assume that only one task can be done at a given time so that the overall time to completion is the sum of the individual task times. We tell the customer that they get a discount if the service takes us more than k×n×M hours. What value for k should we use to ensure that there is a 90% chance that the customer pays full price?

math   Statistics-And-Probability   
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