Managers of the retail stores opening in a new mall in a mid

Managers of the retail stores opening in a new mall in a mid-size Midwestern city face many decisions. They must determine what inventory levels they are going to carry, how the merchandise is best displayed, how advertising campaigns can be used most effectively, what their pricing policies must be as well as an entire list of many other business matters that will have a direct effect on the stores’ bottom lines.

As if all that wasn\'t enough each establishment must concern itself with crime prevention. Here again they find themselves facing many critical decisions. Losses due to unlawful activities can originate from within the organization due to employee theft and embezzlement as well as illegal practices committed by customers and other outsiders.

As owner and director of security operations for Crime Prevention, Incorporated you have been retained by mall authorities to offer your services and advice in the effort to curtail losses due to unlawful activities. You must address each concern of all those store owners and managers, and apply your expertise in the crime prevention field. Each store has its own set of unique concerns regarding illegal activity.

Several of the merchants consulted local police records and found that retail establishments report a monthly average of 17 burglaries that seem to follow a Poisson distribution. These stores plan to open in exactly two weeks. If the likelihood that five or more of the stores will experience a break-in exceeds 10%, they intend to hire additional security forces. Would you advise them to do 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.

Answer:

As the burgalaries are following the Poisson distribution Then we have:

Probability = e ^-mean mean^x / x!

here we have mean = 17

and x = 5

therefore we have

Probability = 0.00045 which is way less than the probability 10% to take any action. So my advice would be status quo.