Formulate the outline of a precision pricing policy for a four-star hotel designed to accommodate business guests as well as tourists from all over the world. Explain your answer

A car salesman tells you that the model you are looking at gets on average 36 miles per gallon overall (highway and street driving) with a standard deviation of 4 miles per gallon. He also tells you that 20% of the cars get at
least 44 miles per gallon.

a. ( Do you think this is a normal distribution? Explain why or why not. (there is no one right answer for this)

b. Analyze the salesman's statement mathematically. Is he being at all untruthful?

i. Explain under the assumption that the distribution IS a normal distribution.

ii. Explain under the assumption that the distribution is NOT a normal distribution.

According to the U.S. Federal Highway Administration, the mean number of miles driven annually is 12,200 with a standard deviation of 3800 miles. A resident of the state of Montana believes the drivers in Montana drive more than the national average. She obtains a random sample of 35 drivers from a list of registered drivers in the state and finds the mean number of miles driven annually for these drivers to be 12,895.90. Is there sufficient evidence to show that residents of the state of Montana drive more than the national average?

What is the p-value for this hypothesis test?
What is the test statistic for this hypothesis test?
What is the critical value?
What is the decision?

The mean tread life of a manufacturer's best selling tire is known to be 22,560 miles. Because the distribution of individual tire life is positively skewed, it cannot be assumed to be normal. R&D has come up with a new rubber additive that they suspect will increase mean tire life without affecting variability of tire life. A sample of 36 tires with the new additive has a sample mean tread life of 24,470 miles; the sample based estimate of the standard deviation is 1200 miles. At .05 level of significance, test whether the additive is working. Clearly state your hypothesis and conclusion.

The tread life (x)  of tires follow  normal distribution with µ =  60,000 and σ= 6000 miles.  The manufacturer guarantees the tread life for the first 52,000 miles. (i) What proportion of tires last  at least 55,000 miles? (ii)  What proportion of the tires will need to be replaced under warranty? (iii)  If you buy 36 tires,  what is the probability that the  average life of your 36 tires will exceed  61,000?  (iv) The manufacturer is willing to replace only 3% of its tires under a warranty program involving tread life.  Find the tread life covered under the warranty.

13. Calculate the expected loss EL if k = $22,000, sigma = 0.7 and D = 0.5.

14. A total of 10 units were tested over a 500-hour period. A total of 4 units failed after 10, 20, 70, and 400 hours. The other 6 did not fail during the 500-hour test. Calculate the failure rate.

15. The mean life of a diesel is 250,000 miles, with a standard deviation of 2,500 miles. What is the probability that it will wear out before 248,000 miles.

16. A component has a reliability of 0.99 for 600 hours of normal use. Determine the failure rate.

What is the NPV for the car selection example below?

Example: Buy an Electric Vehicle?

Chevy Malibu: $30,000 cost  12K miles/yr  30 mph  Maintenance: $1K in year 1; 5% CAGR  Resale of $5K in ten years  Gas: $3.50/g; 10% CAGR  D = 7% 

Nissan Leaf: $40,000 cost  12K miles/yr  5 miles per kWh  Maintenance: $700 in year 1; 5% CAGR  New battery in year 5: $5,000  Resale of $3K in ten years  $0.11/kWh; 10% CAGR  D = 7%

Pleasanton Studios Kersten Brown, the CEO of Pleasanton Studios, is having a tough week – all three of her top management level employees have dropped in with problems. One executive is making questionable decisions, another is threatening to quit, and the third is reporting losses (again). Kersten is hoping to find simple answers to all her difficulties. She is asking you (her accountant) for some advice on how to proceed. Pleasanton Studios owns and operates three decentralized divisions: Entertainment, Streaming, and Parks. Pleasanton Studios has a decentralized organizational structure, where each division is run as an investment center. Division managers meet with the CEO at least once annually to review their performance, where each division manager’s performance is measured by their division’s return on investment (ROI). The division manager then receives a bonus equal to 10% of their base salary for every ROI percentage point above the cost of capital. The Entertainment division manager, John Freeman, was the first to knock on Kersten’s door this morning. Entertainment, Pleasanton Studios’ first endeavor, produces movies for the big screen. Entertainment has been in operation since 1965. Last month, John had mentioned a proposal to build a new animation studio. The build would cost $4,910,000 with an estimated life of 20 years and no salvage value and would allow Entertainment to start producing animated movies. Animated movies were projected to bring in an additional $1,210,000 in revenues each year, but would increase annual production costs by $574,000. John had dropped in to let Kersten know he had decided not to move forward with the animation studio. This surprised Kersten – her quick mental calculation indicated that the studio would have a payback period of 8 years, much shorter than the expected life of the studio. Not entirely sure that her quick assessment was valid, Kersten needed to check with her accountant on the matter. Next to Kersten’s door was the manager of Streaming, which produces short-form (30 minute to one hour) episodes in addition to streaming the movies developed by Entertainment. Customers then buy subscriptions to the service. Run by division manager Reyna Imanah, Streaming was introduced in 2016 and has increased subscriptions by 20% every year since. Reyna’s complaint was that, based on the current bonus payout schedule, John Freeman’s bonus last year was significantly higher than hers. She points to the increasing subscription rates at Streaming, and says that her division is being punished for having opened so recently (her division’s facilities are much more recent than those in Entertainment). She currently has an employment offer from another company at the same base pay rate, and stated that she will accept this offer unless she feels her performance is being appropriately acknowledged and compensated. Kersten needs to look at the relative performance across divisions to determine how to proceed with Reyna. Pleasanton Parks is a theme park based on the movies from Entertainment and the series from Streaming. For many years, it was a popular year-round destination, with characters, rides, and a hotel. This park has lost popularity in recent years, and has been ‘in the red’ for the past two years. If the park is not profitable this year, you will need to decide whether to permanently close that division. Included in the ‘Fixed COGS’ for Parks is an annual $1,650,000 mortgage payment on the land and buildings for the park, which would still need to be paid (as a corporate level cost) if the park is closed and that segment is removed from the financial statements. Incidentally, you recently had a conversation with a Marriott Hotels executive, who would like to expand into the area. If you decided to close Parks, you are fairly certain that you could lease the hotel facilities to Marriott for $650,000 annually. A partial report of this year’s financial results for Pleasanton Studios can be found in Table 1 below. The ‘Selling and admin costs’ listed in Table 1 are directly incurred by each division, and are determined at the beginning of each year (that is, they do not change with increased/decreased production). In addition to the divisional information above, there are $2,000,000 in corporate costs that are currently allocated evenly between the three divisions. These costs are primarily due to employee benefits costs, which are billed at the corporate level. If the Parks division is closed, the decreased employee base would reduce allocated corporate costs by $500,000. Pleasanton Studios has a cost of capital of 12 percent (and Kersten uses the cost of capital as their required rate of return) and are subject to 32% income taxes. Before she can make any decisions, Kersten needs to evaluate this year’s performance results. She sets off to see you, the company’s accountant, for answers.

Required: Write your response in the form of a 1-2 page memo to Kersten Brown, from the perspective of the company accountant. Be sure to include all the financial analyses to support your conclusions, clearly showing your calculations, at the end of the memo or attached in a separate document. Be sure to address the following points in your memo.

a. Evaluate this year’s performance results for the three divisions. Your financial analysis should include a segmented income statement for Pleasanton Studios, as well as the current annual ROI, residual income and EVA for the three divisions.

b. Evaluate Entertainment’s decision not to invest in the new animation studio (i.e., was the decision appropriate and in the best interests of Pleasanton Studios), including the appropriate financial analyses to support your evaluation.

c. Evaluate the validity of Reyna Imanah’s complaint regarding her evaluated performance. Explain why it is (or is not valid), and what further information would be necessary.

d. Provide a recommendation on whether to close the Parks division, including all necessary financial analyses.

Suppose that the manager of the MileagePlus frequent flier program is promoted and consequently another individual is hired to replace him. Also suppose that United publishes in internal documentation that the average number of Premier Qualifying Miles (PQM) earned by individuals who travel for work at least once a month is 45,000 with a standard deviation of 5,000 miles. Further suppose that the new manager desires to test the claims that United has made to see if the statistics have changed.

a) First, are these statistics given by United describing the parent population or a sample ?

b) Define appropriate null and alternative hypothesis

c) Suppose that the new manager takes a sample of 50 such United customers. What is the probability that a sample of size 50 provides a sample mean within + - 1,000 miles of the 45,000 mile figure provided by United?

d) What is the probability that a sample of 50 such United customers provides a sample mean wiithin + - 500 miles?

e) Suppose that the new manager's sample has a sample average of 47,500 miles. Compute the 95% confidence interval for the population mean.

f) Based on the confidence interval you computed in part e), does this sample provide evidence for or against United's claim that the average number of Premier Qualifying Miles (PQM) earned is 45,000 ?

g) If the new manager wants to determine a specific p-value for the likelihood that the null hypothesis is true based on the sample collected in part c), should he use Z- or t- scores for the test statistic?

h) Determine and interpret the p-value

Almost all U.S. light-rail systems use electric cars that run on tracks built at street level. The Federal Transit Administration claims light-rail is one of the safest modes of travel, with an accident rate of .99 accidents per million passenger miles as compared to 2.29 for buses. The following data show the miles of track and the weekday ridership in thousands of passengers for six light-rail systems.

1. Use these data to develop an estimated regression equation that could be used to predict the ridership given the miles of track.
   
   Compute b₀ and b₁ (to 2 decimals).
   b₁   
   b₀   
   
   Complete the estimated regression equation (to 2 decimals).
   =   +  x
   
2. Compute the following (to 1 decimal):

   SSE
   SST
   SSR
   MSE

   
   
3. What is the coefficient of determination (to 3 decimals)? Note: report r² between 0 and 1.
     
   
   Does the estimated regression equation provide a good fit?
   SelectYes, it even provides an excellent fitYes, it provides a good fitNo, it does not provide a good fitItem 10  
   
4. Develop a 95% confidence interval for the mean weekday ridership for all light-rail systems with 30 miles of track (to 1 decimal).
   (  ,   )
   
5. Suppose that Charlotte is considering construction of a light-rail system with 30 miles of track. Develop a 95% prediction interval for the weekday ridership for the Charlotte system (to 1 decimal).
   (  ,   )