The French boutique owned by Ilsa Lund has experienced unusual levels of employee theft at other outlets that have been open for several months prior to the one located in the new mall. According to the reports Ilsa has studied, 85% of retail employees engage in some level of theft, no matter how small (see the Prologue). Ilsa intends to employ 20 sales personnel. If the number of dishonest employees exceeds seven, Ilsa feels it will be necessary to purchase expensive insurance to protect her against such losses. What can you tell her about the wisdom of doing so?

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.

Prepare a Formal Statistical Report of Your Findings.