Suppose that the miles-per-gallon (mpg) rating of passenger cars is a normally distributed random variable with a mean and standard deviation of 33.8 and 3.5 mpg, respectively.

a. What is the probability that a randomly selected passenger car gets more than 35mpg?

b. a random sample of twenty-five passenger cars is selected. Denote Xbar as the sample average mpg of this twenty-five. What is the mean and standard deviation of Xbar?

c. What is the probability that the average mpg of twenty-five randomly selected passenger cars is more than 35 mpg?

The Bahamas is a tropical paradise made up of 700 islands sprinkled over 100,000 square miles of the Atlantic Ocean. According to the figures released by the government of the Bahamas, the mean household income in the Bahamas is $34,627 and the median income is $31,880. A demographer decides to use the lognormal random variable to model this nonsymmetric income distribution. Let Y represent household income, where for a normally distributed X, Y = e^X. In addition, suppose the standard deviation of household income is $11,000. Use this information to answer the following questions. [You may find it useful to reference the z table.]

a. Compute the mean and the standard deviation of X. (Round your intermediate calculations to at least 4 decimal places and final answers to 4 decimal places.)

b. What proportion of the people in the Bahamas have household income above the mean? (Round your intermediate calculations to at least 4 decimal places, “z” value to 2 decimal places, and final answer to 4 decimal places.)

c. What proportion of the people in the Bahamas have household income below $14,000? (Round your intermediate calculations to at least 4 decimal places, “z” value to 2 decimal places, and final answer to 4 decimal places.)

d. Compute the 90th percentile of the income distribution in the Bahamas. (Round your intermediate calculations to at least 4 decimal places, “z” value to 3 decimal places, and final answer to the nearest whole number.)

4. Listed below are the combined city – highway fuel consumption ratings (in miles per gallons) for different cars measured in old rating system and cars in a new rating system introduced in 2008 (based on data from USA today). A. Construct a 90 percent confidence interval of the difference in the ratings of cars. (Use 3 decimal places) (10 pts) Old Rating: 16 18 27 17 33 28 33 18 24 19 18 27 22 18 20 29 19 27 20 21 New Rating: 15 16 24 15 29 25 29 16 22 17 16 24 20 16 18 26 17 25 18 19 B. Based on the interval is there a reason to believe that there is a difference in the ratings of the two cars? C. Is there any significant difference in the old and new ratings of cars? Use appropriate hypothesis test to answer this question.

Authentic Car Services is the only transportation provider in a midsized county, about 65 miles outside of a major city. Licensed by the local government, the firm provides door to door service between the residents’ homes, the train station (which connects to the major city), local retail stores, and other key locations within and surrounding the town center. To access the service, residents may call for a specific pick-up time, or they could wait by any curb for an unscheduled curbside pick-up.

The market demand for transportation services is described by the equations: P = 8 – 0.015Q and MR = 8 – 0.03Q, where Q is the number of trips per week.

With regular maintenance on its fleet of vehicles as well as outstanding loan payments, the firm faces a weekly fixed cost of $200.

Authentic Car Services’ labor force includes drivers and dispatchers, and all report to work if the firm is providing service. Along with the labor force and the necessary materials needed for day-to-day operation, the firm’s additional costs can be described by the equations: MC = 2 + 0.01Q and AVC = 2 + 0.005Q, where Q is the number of trips per week.

1. Currently, Authentic Car Services provides _________ trips per week and charges $_________ for each trip.

2. At the current profit-maximizing quantity, Authentic Car Services’ profit is $______ per week.

3. The current market outcome ______ (either is or is not | is | is not ) efficient and a measure of this ______ (efficiency | efficiency or inefficiency | inefficiency) is $ _______.

Now consider that consumers’ income increases, and transportation services is a normal good. As a result, the new market demand for transportation services is described by one of the following equation sets:

Equation A: P = 7 – 0.015Q, and MR = 7 – 0.03Q

Equation B: P = 10 – 0.015Q and MR = 10 – 0.03Q

The market fully adjusts after the demand shock.

4. As a result of the shock, the new market demand is described by Equation ____ (A | B) .  Authentic Car Services now provides ______ trips per week and charges $_____ for each trip.

5. As a result of the shock, consumers’ surplus has decreased. Now, Authentic Car Services has _________ (a higher | a lower | no change in its) economic profit, and the overall market _______ (efficiency | efficiency or inefficiency | inefficiency) has _________ (decreased to | increased to | remains the same at ) $.___________.

Lon Timur is an accounting major at a midwestern state university located approximately 60 miles from a major city. Many of the students attending the university are from the metropolitan area and visit their homes regularly on the weekends. Lon, an entrepreneur at heart, realizes that few good commuting alternatives are available for students doing weekend travel. He believes that a weekend commuting service could be organized and run profitably from several suburban and downtown shopping mall locations. Lon has gathered the following investment information.

(a)

Determine the annual (1) net income and (2) net annual cash flows for the commuter service. (Round answers to 0 decimal places, e.g. 125.)

(b)

Compute (1) the cash payback period and (2) the annual rate of return. (Round answers to 2 decimal places, e.g. 10.50.)

(c)

Compute the net present value of the commuter service. (Round answer to 0 decimal places, e.g. 125. If the net present value is negative, use either a negative sign preceding the number eg -45 or parentheses eg (45). For calculation purposes, use 5 decimal places as displayed in the factor table provided.)

2A Lon Timur is an accounting major at a midwestern state university located approximately 60 miles from a major city. Many of the students attending the university are from the metropolitan area and visit their homes regularly on the weekends. Lon, an entrepreneur at heart, realizes that few good commuting alternatives are available for students doing weekend travel. He believes that a weekend commuting service could be organized and run profitably from several suburban and downtown shopping mall locations. Lon has gathered the following investment information. 1. Five used vans would cost a total of $75,000 to purchase and would have a 3-year useful life with negligible salvage value. Lon plans to use straight-line depreciation. 2. Ten drivers would have to be employed at a total payroll expense of $48,000. 3. Other annual out-of-pocket expenses associated with running the commuter service would include Gasoline $16,010, Maintenance $3,300, Repairs $4,000, Insurance $4,210, and Advertising $2,510. 4. Lon has visited several financial institutions to discuss funding. The best interest rate he has been able to negotiate is 15%. Use this rate for cost of capital. 5. Lon expects each van to make ten round trips weekly and carry an average of six students each trip. The service is expected to operate 30 weeks each year, and each student will be charged $11.95 for a round-trip ticket. Click here to view PV table. (a) Determine the annual (1) net income and (2) net annual cash flows for the commuter service. (Round answers to 0 decimal places, e.g. 125.) Net income $ Net annual cash flows $ (b) Compute (1) the cash payback period and (2) the annual rate of return. (Round answers to 2 decimal places, e.g. 10.50.) Cash payback period years Annual rate of return % (c) Compute the net present value of the commuter service. (Round answer to 0 decimal places, e.g. 125. If the net present value is negative, use either a negative sign preceding the number eg -45 or parentheses eg (45). For calculation purposes, use 5 decimal places as displayed in the factor table provided.) Net present value

Can we predict the running time for Mr. Degges when he runs 3.1 miles on the track at the NDSU Wellness center?

Need: SAS output to analyze the model

Need: prediction equation

y-hat

SSE SST, error, F-test

What variables are significant

The variables are: Y = running time in minutes X1 = weight at the time of running X2 = number of days between running events

Year X1 X2   Y

2009 191.2 1 29.0

2009 192 1   27.80

2009 190.4 2 28.53

2009 190.4 3 28.10

2009 190.6 2   28

2009 190.6 0   27.43

2009 190.2 0 28

2009 191.8 1    27.27

2009 189.2 12 30.52

2009 189.2 0 28.95

2009 190.2 2 29.08

2015 168.6 14 29.92

2015 166.2 4   29.83

2015 165.0 2 28.37

2015 169.8 6 27.25

2015 169.4 4 27.85

2015 167.2 3 27.58

2015 166.6 2 27.10

You are driving at 90 miles/hour.  You suddenly see a Police car on the shoulder at 100 meters. How hard you need to hit the break (what should be your deceleration) to reduce you speed from 90 mi/h to 60 mil/s at the time you reach to the officer? Your reaction time, before stepping on the brake is 0.50 s 1 mile/h = 0.45 m/s

In 1974, the United States instituted a national speed limit of 55 miles per hour (mph), a move that generated a great deal of controversy. Proponents of the lower speed limit managed to avoid repeal of this national speed limit by effectively arguing that driving at 55 mph significantly reduced the number of traffic fatalities on U.S. highways. The argument was based on the fact that the total number of traffic fatalities dropped from 55,511 in 1973 to only 46,402 in 1974. Because people have questioned the validity of this argument, you are going to examine more rigorously the hypothesis that the reduction in fatalities was due to the institution of the 55 mph speed limit.

Procedure. Since the change to a 55 mph speed limit occurred a number of years ago, you must use archival data in your study. The U. S. government routinely makes available a wide variety of data on the U.S. population. Most public and private libraries either own or would be able to get the national or state statistics you need. Here is the data you would obtain for the present research question:

Table 1: Annual Traffic Fatalities on U.S. Highways

Year Number of fatalities

1966 53,041

1967 52,924

1968 55,200

1969 55,791

1970 54,633

1971 52,660

1972 56,278

1973 55,511

1974 46,402

1975 45,853

1976 47,038

1977 49,510

1978 50,226

Source: U.S. National Center for Health Statistics, Vital Statistics of the United States, annual.

One process of policy implementation decision is the rational comprehensive decision making process. Optimum decisions are the goal. While most of the literature and focus is on economic analysis of optimality, we also need to consider social optimality. Part of that process is through empirical analysis of data and determining its validity. Our knowledge of research designs can be a valuable tool. The purpose of this case analysis is to use those tools.

The hypothesis for this policy implementation analysis is the reduction in fatalities was due to the institution of the 55 mph speed limit. Using about 1000 words (three pages of discussion) and at least 3 scholarly references (one can be the text), review this case and respond to the questions:

What kind of threats to internal validity do these events represent?
Is this policy effective? Does the increasing number of fatalities after 1974 have any implications for the effectiveness of the speed limit intervention?
What is/are one or more of the rival explanations?
What would be at least one social cost of this policy? How is it defined and measured?
What decision making theory was used? What theory should have been used?
As a final paragraph, conclude how this case discussion can assist public administrator's decision making in their role as implementing policy.

An automobile manufacturer claims that their jeep has a 34.7 miles/gallon (MPG) rating. An independent testing firm has been contracted to test the MPG for this jeep. After testing 250 jeeps they found a mean MPG of 35.0. Assume the standard deviation is known to be 1.6. Is there sufficient evidence at the 0.02 level that the jeeps have an incorrect manufacturer's MPG rating?

Step 4 of 5: Enter the decision rule.