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Chapter 4: Probability: An Introduction to Modeling Uncertainty: Case Problem 2 McNeil’s Auto Mall Book Title: Business Analytics Printed By: Jigar Jitendrak Patel ([email protected]) © 2021 Cengage Learning, Cengage Learning
Chapter Review
Case Problem 2 McNeil’s Auto Mall
Harriet McNeil, proprietor of McNeil’s Auto Mall, believes that it is good business for herautomobile dealership to have more customers on the lot than can be served, as shebelieves this creates an impression that demand for the automobiles on her lot is high.However, she also understands that if there are far more customers on the lot than can beserved by her salespeople, her dealership may lose sales to customers who becomefrustrated and leave without making a purchase.
Ms. McNeil is primarily concerned about the staffing of salespeople on her lot on Saturdaymornings (8:00 a.m. to noon), which are the busiest time of the week for McNeil’s Auto Mall.On Saturday mornings, an average of 6.8 customers arrive per hour. The customers arriverandomly at a constant rate throughout the morning, and a salesperson spends an averageof one hour with a customer. Ms. McNeil’s experience has led her to conclude that if thereare two more customers on her lot than can be served at any time on a Saturday morning,her automobile dealership achieves the optimal balance of creating an impression of highdemand without losing too many customers who become frustrated and leave withoutmaking a purchase.
Ms. McNeil now wants to determine how many salespeople she should have on her lot onSaturday mornings in order to achieve her goal of having two more customers on her lotthan can be served at any time. She understands that occasionally the number of customerson her lot will exceed the number of salespersons by more than two, and she is willing toaccept such an occurrence no more than 10% of the time.
Managerial Report
Ms. McNeil has asked you to determine the number of salespersons she shouldhave on her lot on Saturday mornings in order to satisfy her criteria. In answeringMs. McNeil’s question, consider the following three questions:
1. How is the number of customers who arrive in the lot on a Saturdaymorning distributed?
2. Suppose Ms. McNeil currently uses five salespeople on her lot on Saturdaymorning. Using the probability distribution you identified in (1), what is theprobability that the number of customers who arrive on her lot will exceedthe number of salespersons by more than two? Does her current Saturday
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morning employment strategy satisfy her stated objective? Why or whynot?
3. What is the minimum number of salespeople Ms. McNeil should have onher lot on Saturday mornings to achieve her objective?
Chapter 4: Probability: An Introduction to Modeling Uncertainty: Case Problem 2 McNeil’s Auto Mall Book Title: Business Analytics Printed By: Jigar Jitendrak Patel ([email protected]) © 2021 Cengage Learning, Cengage Learning
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