Almost all medical schools in the United States require students to take the Medical College Admission Test (MCAT). To estimate the mean score ?μ of those who took the MCAT on your campus, you will obtain the scores of an SRS of students. The scores follow a Normal distribution, and from published information you know that the standard deviation is 10.410.4 . Suppose that, unknown to you, the mean score of those taking the MCAT on your campus is 500500 .

In answering the questions, use ?z‑scores rounded to two decimal places.

(a) If you choose one student at random, what is the probability that the student's score is between 495495 and 505505 ? Use Table A, or software to calculate your answer.

(Enter your answer rounded to four decimal places.)

probability:

(b) You sample 2525 students. What is the standard deviation of the sampling distribution of their average score ?¯x¯ ? (Enter your answer rounded to two decimal places.)

standard deviation:

(c) What is the probability that the mean score of your sample is between 495495 and 505505 ? (Enter your answer rounded to four decimal places.)

probability:

High school graduates: Approximately 78% of freshmen entering public high schools in the United States in 2005 graduated with their class in 2009. A random sample of 128 freshmen is chosen.

(a)Find the mean μp

.(b)Find the standard deviation σp

.

(c)Find the probability that less than 91% of freshmen in the sample graduated.

(d)Find the probability that between 68%and 83% of freshmen in the sample graduated.

(e)Find the probability that more than 68%of freshmen in the sample graduated.Cumulative Normal Distribution Table as needed. Round your answers to at least four decimal places if necessary.

High school graduates: Approximately

78%

of freshmen entering public high schools in the United States in

2005

graduated with their class in

2009

. A random sample of

128

freshmen is chosen. Use

(a)Find the mean

μp

.(b)Find the standard deviation

σp

.

(c)Find the probability that less than

91%

of freshmen in the sample graduated.

(d)Find the probability that between

68%

and

83%

of freshmen in the sample graduated.

(e)Find the probability that more than

68%

of freshmen in the sample graduated.

Cumulative Normal Distribution Table as needed. Round your answers to at least four decimal places if necessary.

High school graduates: Approximately

74%

of freshmen entering public high schools in the United States in

2005

graduated with their class in

2009

. A random sample of

175

freshmen is chosen. Use Cumulative Normal Distribution Table as needed. Round your answers to at least four decimal places if necessary.

(a)Find the mean

μp

.

Part 2 of 6

(b)Find the standard deviation

σp

.

Part 3 of 6

(c)Find the probability that less than

75%

of freshmen in the sample graduated.

Part 4 of 6

(d)Find the probability that between

64%

and

78%

of freshmen in the sample graduated.

Part 5 of 6

(e)Find the probability that more than

64%

of freshmen in the sample graduated.

Part 6 of 6

(f)Would it be unusual if the sample proportion of freshmen in the sample graduated was more than

83%

?

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.

The production capacity for acrylonitrile (C₃H₃N) in the United States exceeds 2 million pounds per year. Acrylonitrile, the building block for polyacrylonitrile fibers and a variety of plastics, is produced from gaseous propylene, ammonia, and oxygen.

2 C₃H₆(g) + 2 NH₃(g) + 3 O₂(g) → 2 C₃H₃N(g) + 6 H₂O(g)

(a) What mass of acrylonitrile can be produced from a mixture of 1.22 kg of propylene (C₃H₆), 1.62 kg of ammonia, and 1.87 kg of oxygen, assuming 100% yield?

The production capacity for acrylonitrile (C3H3N) in the United States exceeds 2 million pounds per year. Acrylonitrile, the building block for polyacrylonitrile fibers and a variety of plastics, is produced from gaseous propylene, ammonia, and oxygen. 2 C3H6(g) + 2 NH3(g) + 3 O2(g) → 2 C3H3N(g) + 6 H2O(g) (a) What mass of acrylonitrile can be produced from a mixture of 1.16 kg of propylene (C3H6), 1.65 kg of ammonia, and 1.78 kg of oxygen, assuming 100% yield? (b) What mass of water is produced? (c) What mass of oxygen is left in excess?

The United States has sent extremely large numbers of troops to countries like Iraq and Afghanistan over the past decade. Record numbers of soldiers returning from combat duty in the Middle East have been diagnosed as suffering from posttraumatic stress disorder (PTSD).

Considering our understanding of PTSD, why do you imagine these figures have grown so rapidly over the last few years? What might be possible treatment options for addressing this matter? Explain.

Suppose that the United States and Saudi Arabia can each produce two products, oil and personal computers. The labor requirements per unit of output are provided in the table below:

Calculate the labor and opportunity costs for each good, and then compute each country’s absolute and comparative advantage. Use the results to determine what good each country should export and explain your reasoning.

1. What does absolute advantage mean? How do you calculate absolute advantage?
2. Which country has an absolute advantage in producing oil? Explain using the data from the table.
3. Which country has an absolute advantage in producing personal computers? Explain using the data from the table.
4. What does comparative advantage mean? How do you calculate comparative advantage?
5. In what output(s) does the U.S. have a comparative advantage? Explain using the data from the table.
6. In what output(s) does Saudi Arabia have a comparative advantage? Explain using the data from the table.
7. What product should each country export? Why

Lionel Corporation manufactures pharmaceutical products sold through a network of sales agents in the United States and Canada. The agents are currently paid an 18% commission on sales; that percentage was used when Lionel prepared the following budgeted income statement for the fiscal year ending June 30, 2019:

Since the completion of the income statement, Lionel has learned that its sales agents are requiring a 5% increase in their commission rate (to 23%) for the upcoming year. As a result, Lionel’s president has decided to investigate the possibility of hiring its own sales staff in place of the network of sales agents and has asked Alan Chen, Lionel’s controller, to gather information on the costs associated with this change.

Alan estimates that Lionel must hire eight salespeople to cover the current market area, at an average annual payroll cost for each employee of $80,000, including fringe benefits expense. Travel and entertainment expenses is expected to total $600,000 for the year, and the annual cost of hiring a sales manager and sales secretary will be $150,000. In addition to their salaries, the eight salespeople will each earn commissions at the rate of 10% of sales. The president believes that Lionel also should increase its advertising budget by $500,000 if the eight salespeople are hired.

Required

-Determine Lionel’s breakeven point (operating profit = 0) in sales dollars for the fiscal year ending June 30, 2019, if the company hires its own sales force and increases its advertising costs. Prove this by constructing a contribution income statement.

-If Lionel continues to sell through its network of sales agents and pays the higher commission rate, determine the estimated volume in sales dollars that would be required to generate the operating profit as projected in the budgeted income statement.

-Describe the general assumptions underlying breakeven analysis that may limit its usefulness.

-What is the indifference point in sales for the firm to either accept the agents' demand or adopt the proposed change? Determine which plan is better for the firm.

-Are there ethical issues?