the accompanying data represent the miles per gallon of a random sample of cars with a​ three-cylinder, 1.0 liter engine. ​(a) compute the​ z-score corresponding to the individual who obtained 38.7 miles per gallon. interpret this result. ​(b) determine the quartiles. ​(c) compute and interpret the interquartile​ range, iqr. ​(d) determine the lower and upper fences. are there any​ outliers?39.939.9 42.442.4 34.634.6 36.336.3 38.138.1 38.938.9 40.540.5 42.842.8 34.734.7 37.537.5 38.338.3 39.439.4 41.441.4 43.643.6 35.235.2 37.637.6 38.538.5 39.739.7 41.641.6 49.049.0

Comment on the relationship between 1920s-1940s economics and today's economic conditions. Are there any similarities that you notice? Any key differences?

Donna Shader, manager at the Winter Park Hotel, is considering how to restructure the front desk to reach an optmum level of staff efficiency and guest service. Presently, the hotel has five clerks on duty, each with a separate waiting line, during the peak check in time of 3:00 P.M to 5:00 P.M.

Observation of arrivals during this time show that an average of 90 guests arrive each hour (although there is no upward limit on the number that could arrive at any given time). It takes an average of 3 minutes for the front-desk clerk to register each guest.

Donna is considering three plans for improving guest service by reducing the length of time guests spend waiting in line.

The first proposal would designate on employee as a quick service clerk for guests registering under corporate accounts, a market segment that fills about 30% of all occupied rooms. Because corporate guests are preregistered, their registration takes just 2 minutes. With these guests separated from the rest of the clientele, the average time for registering a typical guest would climb to 3.4 minutes. Under plan 1, noncorporate guests would choose any of the remaining four lines.

The second plan is to implement a single line system. All guests could form a single waiting line to be served by whichever of the five clerks became available. This option would require sufficient lobby space for what could be a substantial queue.

The third proposal using an automatic teller machine (ATM) for check-ins. This ATM would provide approximately the same service rate as a clerk would. Given that initial use of this technology might be minimal, Shader estimated that 20% of customers, primarily frequent guests, would be willing to use the machines.

(This might be a conservative estimate if the guests perceive direct benefits from using the ATM, as bank customers do. Citibank reports that 95% of its Manhattan customers use its ATMs.) Donna would set up a single queue for customers who prefer human check-in clerks. This would be served by the five clerks although Donna is hopeful that the machine will allow a reduction to four.

Required:

1. Determine the average amount of time that a guest spends checking in.
2. What is the check in time under each plan?
3. What plan would you recommend.

2. Courtney Newell, manager of the Silver Park Hotel, is considering how to restructure the front desk to improve guest service during the peak check-in hours of 3:00 to 5:00 p.m. At present, the hotel has 5 clerks on duty each with a separate waiting line.

Courtney is considering two plans for reducing the guest’s waiting time. The first proposal would be to implement a single waiting line in which guests would be served by whichever of the 5 clerks becomes available first. Observations of arrivals during the peak check-in time show that a guest arrives on average every 40 seconds. It takes an average of 3 minutes for the front-desk clerk to register each guest.

The second proposal would designate one employee as a “quick-service” clerk for guests registering under corporate accounts, a market segment that comprises about 30% of Silver Park’s guests. Since these guests would be pre-registered, it would take an average of only 0.5 minutes for the front-desk clerk to register them. Under this plan, the non-corporate guests would form a single line and proceed to the first available of the 4 remaining clerks. The average time for registering a non-corporate guest is 3.4 minutes.

Which proposal should Courtney implement? Provide appropriate quantitative evidence to support your recommendation.

1. Courtney Newell, manager of the Silver Park Hotel, is considering how to restructure the front desk to improve guest service during the peak check-in hours of 3:00 to 5:00 p.m.  At present, the hotel has 5 clerks on duty each with a separate waiting line.

Courtney is considering two plans for reducing the guest’s waiting time. The first proposal would be to implement a single waiting line in which guests would be served by whichever of the 5 clerks becomes available first.  Observations of arrivals during the peak check-in time show that a guest arrives on average every 40 seconds.  It takes an average of 3 minutes for the front-desk clerk to register each guest.

The second proposal would designate one employee as a “quick-service” clerk for guests registering under corporate accounts, a market segment that comprises about 30% of Silver Park’s guests.  Since these guests would be pre-registered, it would take an average of only 0.5 minutes for the front-desk clerk to register them.  Under this plan, the non-corporate guests would form a single line and proceed to the first available of the 4 remaining clerks.  The average time for registering a non-corporate guest is 3.4 minutes.

Which proposal should Courtney implement?  Provide appropriate quantitative evidence to support your recommendation.

1. A rancher owns 500 acres of land which is suitable for growing sorghum, corn, and wheat. She expects net profits per acre from each crop to be: $55 for sorghum, $60 for corn, and $50 for wheat. She is able to supply 3,000 hours per year of on-farm labor. Additionally, she has 4,500 hours of tractor time available for the production of these three crops. The requirements of each crop are summarized below.

1. Write out the linear programming problem, including the objective function and all constraints. Please represent the problem and constraints in general equation form.

Computers in some vehicles calculate various quantities related to performance. One of these is the fuel efficiency, or gas mileage, usually expressed as miles per gallon (mpg). For one vehicle equipped in this way, the miles per gallon were recorded each time the gas tank was filled, and the computer was then reset. In addition to the computer's calculations of miles per gallon, the driver also recorded the miles per gallon by dividing the miles driven by the number of gallons at each fill-up. The following data are the differences between the computer's and the driver's calculations for that random sample of 20 records. The driver wants to determine if these calculations are different. Assume that the standard deviation of a difference is σ = 3.0.

6.0 7.5 −0.6 1.5 3.7 4.5 6.0 2.2 4.8 3.0

4.4 0.3 3.0 1.1 1.1 5.0 2.1 3.7 −0.6 −4.2

(a) State the appropriate

H₀  and H_a  to test this suspicion.

CORRECT: H₀: μ = 0 mpg;    H_a: μ ≠ 0 mpg

(b) Carry out the test. Give the P-value. (Round your answer to four decimal places.)