Libby Crook, owner of Crook Autos, believes that it is good business for her automobile dealership to have more customers on the lot than can be served, as she believes 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 be served by her salespeople, her dealership may lose sales to customers who become frustrated and leave without making a purchase. Ms. Crooks is primarily concerned about the staffing of salespeople on her lot on Saturday mornings (8:00 a.m. to noon), which is the busiest time of the week. On Saturday mornings, an average of 6.8 customers arrive per hour. The customers arrive randomly at a constant rate throughout the morning, and a salesperson spends an average of one hour with a customer. Ms. Crook’s experience has led her to conclude that if there are 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 high demand without losing too many customers who become frustrated and leave without making a purchase. Ms. Crook now wants to determine how many salespeople she should have on her lot on Saturday mornings in order to achieve her goal of having two more customers on her lot than can be served at any time. She understands that occasionally the number of customers on her lot will exceed the number of salespersons by more than two, and she is willing to accept such an occurrence no more than 10% of the time. Instructions: Ms. Crook has hired you to help determine the number of salespersons she should have on her lot on Saturday mornings in order to satisfy her criteria. To complete the project, answer the following three questions: 1. How is the number of customers who arrive in the lot on a Saturday morning distributed? Explain why you believe this is true. 2. Suppose Ms. Crook currently uses five salespeople on her lot on Saturday morning. Using the probability distribution you identified in (1), what is the probability that the number of customers who arrive on her lot will exceed the number of salespersons by more than two? Does her current Saturday morning employment strategy satisfy her stated objective? Why or why not? 3. What is the minimum number of salespeople Ms. Crook should have on her lot on Saturday mornings to achieve her objective
Contingency Table
A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.
Binomial Distribution
Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.
Libby Crook, owner of Crook Autos, believes that it is good business for her automobile
dealership to have more customers on the lot than can be served, as she believes 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 be served by her
salespeople, her dealership may lose sales to customers who become frustrated and leave
without making a purchase. Ms. Crooks is primarily concerned about the staffing of
salespeople on her lot on Saturday mornings (8:00 a.m. to noon), which is the busiest time of
the week. On Saturday mornings, an average of 6.8 customers arrive per hour. The customers
arrive randomly at a constant rate throughout the morning, and a salesperson spends an
average of one hour with a customer. Ms. Crook’s experience has led her to conclude that if
there are 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
high demand without losing too many customers who become frustrated and leave without
making a purchase. Ms. Crook now wants to determine how many salespeople she should
have on her lot on Saturday mornings in order to achieve her goal of having two more
customers on her lot than can be served at any time. She understands that occasionally the
number of customers on her lot will exceed the number of salespersons by more than two, and
she is willing to accept such an occurrence no more than 10% of the time.
Instructions:
Ms. Crook has hired you to help determine the number of salespersons she should have on her
lot on Saturday mornings in order to satisfy her criteria. To complete the project, answer the
following three questions:
1. How is the number of customers who arrive in the lot on a Saturday morning
distributed? Explain why you believe this is true.
2. Suppose Ms. Crook currently uses five salespeople on her lot on Saturday morning.
Using the probability distribution you identified in (1), what is the probability that the
number of customers who arrive on her lot will exceed the number of salespersons by
more than two? Does her current Saturday morning employment strategy satisfy her
stated objective? Why or why not?
3. What is the minimum number of salespeople Ms. Crook should have on her lot on
Saturday mornings to achieve her objective
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