Delivery times for Mac Trucking, the firm that supplies Rick’s Café American, ar
ID: 3004018 • Letter: D
Question
Delivery times for Mac Trucking, the firm that supplies Rick’s Café American, are normally distributed and average 2.5 hours with a standard deviation of 30 minutes. As costs increase, Sam MacGuiver, owner of the transport company, has become increasing concerned about dwindling profits levels. His first concern rests with delivery times and expenses associated with the deliveries. He has asked you, his able statistical wizard, to address a few of the issues.
Sam initially wants to know how quickly the fastest 20% of the deliveries are handled. Based on this information he can establish a pay scale for his employees.
In addition, if in a given week the company completes 75 deliveries, Sam must compute the total cost of the deliveries if he pays the workers
$150 for deliveries that take less than 1 hour
$100 for deliveries that take between 1 hour and 2 hours
$50 for deliveries that take between 2 and 2.5 hours
$25 for deliveries that take between 2.5 and 3.5 hours
nothing for deliveries that require more than 3.5 hours
The mean delivery time of 2.5 hours also displeases Sam. He is considering a new routing system that will reduce the standard deviation in times to 20 minutes. He wants to know what mean delivery times those new routes would have to produce to ensure that 30% of the deliveries could be made in less than 1.7 hours.
Loading the trucks prior to transport is a matter requiring some attention. Loading times appear to be uniformly distributed ranging from 10 hours to 18 hours for the more delicate merchandise. If loading costs average $50 per hour, Sam must know the average cost for loading each truck and the dispersion in those costs.
Finally, trucks arrive at the loading dock at a Poisson rate of 1.2 per hour. In order to determine the number of loaders he must hire Sam is interested in the probability that less than 2 hours pass between arrivals.
Explanation / Answer
Delivery time is normal (2.5, 0.5)
Fastest delivery z = 0.84
delivery time for fastest 20% = 2.5-0.84(0.5)
= 2.08 hours
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If X is N(2.5, 0.33)
P(X<1.7) = P(Z<-0.242)
=0.5-0.0948=0.4052
>30%
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10 to 18 hours loading time
Hence costs would be spread between 500 and 900 dollars
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