Customers arrive on average every 30 minutes to The Grease Monkey, an auto repair shop with only one mechanic. The inter-arrival times are exponentially distributed. Repair times are variable with a mean of 25 minutes and a standard deviation of 20 minutes. The mechanic works on one vehicle at a time from beginning to end and takes in any waiting vehicles on a first-come first-served basis. The garage itself has room for only one vehicle at a time, so waiting vehicles are kept in the parking lot where there are always plenty of spaces available. Assume customers never balk or renege. a)What is the average number of cars in the garage (not including the parking lot)? b) How long (in minutes) do vehicles wait on average in the adjacent parking lot? c) The competitor shop across the street also has a single mechanic and an average of 3.1 vehicles waiting in its parking lot. The competitor only does oil changes, which take an average of 21 minutes. Customer inter-arrival times to the competitor have a mean of 24 minutes and follow an exponential distribution. What is the standard deviation of the time required for an oil change at the competitor’s shop?
Customers arrive on average every 30 minutes to The Grease Monkey, an auto repair shop with only one mechanic. The inter-arrival times are exponentially distributed. Repair times are variable with a
a)What is the average number of cars in the garage (not including the parking lot)?
b) How long (in minutes) do vehicles wait on average in the adjacent parking lot?
c) The competitor shop across the street also has a single mechanic and an average of 3.1 vehicles waiting in its parking lot. The competitor only does oil changes, which take an average of 21 minutes. Customer inter-arrival times to the competitor have a mean of 24 minutes and follow an exponential distribution. What is the standard deviation of the time required for an oil change at the competitor’s shop?
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