1. (a) If A and B are independent events with P(A) = 0.6 and P(B) = 0.7, find P (A or B).

(b) A randomly selected student takes Biology or Math with probability 0.8, takes Biology and Math with probability 0.3, and takes Biology with probability 0.5. Find the probability of taking Math.

2. A box contains 4 blue, 6 red and 8 green chips.

1. In how many different ways can you select 2 blue, 3 red and 5 green chips? (Give the exact numerical value).

2. Draw two chips in a row without replacement. Find the probability that both chips are green.

3. Based on the following table, compute the probabilities below:

P (Women and Yes) =

P (Men | Yes) =

P (No | Women) =

P (Men or No) =

Are Men and No Opinion mutually exclusive?

Are Men and No Opinion independent? Justify your answer by an appropriate computation.

The following is the recent historical sales of Sony HDTV at a local BestBuy store.

• Solution inputs are numbers only, no symbols or letters such as "$, (2.3), dollar".
• Numbers can be in the format of either 3000 or 3,000; 0.95 or .95
• Keep two decimals if not exact, do not round. For example, 3.24923... will be kept as 3.24, but the exact value of 0.625 will be kept as 0.625

1. Use the naive approach to forecast sales for June.  
2. Use a 4-month simple moving average to forecast sales for June.  
3. Using weighted moving average method, with weights of 0.5 one period ago, 0.3 two periods ago, and 0.2 three periods ago, to forecast sales for June.  
4. Assuming the forecast for April is 60. Use exponential smoothing, with a smoothing constant of 0.2, to forecast sales for June.  
5. Use simple linear regression y=a+bx, to first calculate the parameter value of b , then the parameter value of a  , and finally to forecast sales for June.  

Please evaluate Forecasting Method A, in terms of MAD and TS, based on the following forecasted sales, comparing to the realized actual sales.

• Solution inputs are number and letter only, no symbols such as "A., or (2.3)"
• Numbers can be in the format of either 3000 or 3,000; 0.95 or .95; negative number should be in the format of -0.8 instead of (0.8).
• Keep two decimals if not exact, do not round. For example, 3.24923... will be kept as 3.24, but the exact value of 0.625 will be kept as 0.625

1. The MAD value of forecasting method A is:  
2. The TS value of forecasting method A is:  
3. If another forecasting method B has the MAD = 4, and TS = 0.2, then which forecasting method (A or B) is better in terms of MAD value?   and which forecasting method (A or B) is better in terms of TS value?  

Y = f(k) = k^a, where a = 0.25

S = 0.3

δ = 0.2

n = 0.05

g= 0.02

a. Find the steady state capital per effective worker, output per effective worker, investment per effective worker, and consumption per effective worker.

b. Find the steady state growth rate of capital per worker, output per worker, investment per worker, and consumption per worker.

c. Find the steady state growth rate of capital, output, investment, and consumption.

d. Show using two separate graphs the effects on the Solow growth model (i) an increase in the savings rate, and (ii) and an increase in depreciation rate, the population growth rate, or the technological growth rate.

Consider historical data showing that the average annual rate of return on the S&P 500 portfolio over the past 85 years has averaged roughly 8% more than the Treasury bill return and that the S&P 500 standard deviation has been about 34% per year. Assume these values are representative of investors' expectations for future performance and that the current T-bill rate is 5%.

Calculate the utility levels of each portfolio for an investor with A = 3. Assume the utility function is U = E(r) − 0.5 × Aσ².

Consider historical data showing that the average annual rate of return on the S&P 500 portfolio over the past 85 years has averaged roughly 8% more than the Treasury bill return and that the S&P 500 standard deviation has been about 27% per year. Assume these values are representative of investors' expectations for future performance and that the current T-bill rate is 6%.

Calculate the utility levels of each portfolio for an investor with A = 2. Assume the utility function is U = E(r) − 0.5 × Aσ².

Answer Problems below:

Q1. Mr. Miles is a first time investor and wants to build a portfolio using only U.S. T-bills and an index fund that closely tracks the S&P 500 Index. The T-bills have a return of 5%. The S&P 500 has a standard deviation of 20% and an expected return of 15%.

1. Draw the CML and mark the points where the investment in the market is 0%, 25%, 75%, and 100%.

2. Mr. Miles is also interested in determining the exact risk and return at each point.

Q2. Mr. Miles decides to set aside a small part of his wealth for investment in a portfolio that has greater risk than his previous investments because he anticipates that the overall market will generate attractive returns in the future. He assumes that he can borrow money at 5% and achieve the same return on the S&P 500 as before: an expected return of 15% with a standard deviation of 20%. Calculate his expected risk and return if he borrows 25%, 50%, and 100% of his initial investment amount.

The equation of an ellipse is x2/a2+y2/b2=1, where a and b are positive constants, a ³ b. The foci of this ellipse are located at (c, 0), and (-c, 0), where c = (a² – b²)^1/2. The eccentricity, e, of this ellipse is given by e=c/a, while the length of the ellipse’s perimeter is

  \int_0^((\pi )/(2)) 4a(1-e^(2)sin^(2)\theta )^((1)/(2))d\theta .

If 0 < e < 1, this integral cannot be integrated in terms of “well-known” functions. However, fnInt, may be used to approximate the integral.

The path of the earth lies in a plane, and follows an ellipse, with the sun at one of its foci. It takes one year for the earth to orbit the sun. The closest the earth comes to the sun is 91.5 million miles, and the furthest is 94.5 million miles.

1.      For the earth and sun configuration, what are the values of a, b, c, and e?

2.      How far does the earth travel in one orbit of the sun?

3.      What is the average speed of the earth, around the sun, in miles per second? Why is this the average speed?

1. Suppose it is claimed that the typical adult travels an average distance of 16 miles to get to work each day. You believe this average is too low for Columbus residents. You survey a random sample of 98 adults from Columbus and find that your sample travels an average distance of 17.6 miles to work each day, with a sample standard deviation of 7.8 miles.   Use this information to conduct the appropriate hypothesis test by going through the steps you learned about from our Chapter 22 and Chapter 23 lecture videos (and from your reading of Chapters 22 and 23). Assume the alpha level is .05 (or 5%).

1. What will the hypotheses be?

H_o:

H_a:

2. Use the following formula to compute the test statistic.

3. Based on what you see in Table B, what should the p-value be?

4. Will you reject or fail to reject the null hypothesis? Please state your decision and the reason why you are making that decision.

5. In general, if we end up rejecting the null hypothesis when conducting a hypothesis test, we say our results are __________________ significant.

Accounting Ethics In your role as an internal auditor for a car manufacturer, you discovered that your employer can produce a car engine that will get 8 more miles per gallon than the existing engine. However, the cost of producing this car engine would be an additional $3,000 per car. Assume that a typical driver drives a car for 5 years and 200,000 miles. Also, assume that the cost of a gallon of gas is $5 per gallon and a typical car gets 24 miles per gallon. The company is wondering if it is ethical to not produce this more efficient engine. a. Is this an ethical question or just a simple cost accounting problem? b. How would you analyze this from the perspective of shareholder theory? c. How would you analyze this from the perspective of stakeholder theory? d. If this car manufacturer does decide to produce the more fuel-efficient car, would you consider it to be an act of corporate social responsibility? e. Would your answer to the preceding question be different if the car manufacturer's motivation was simply to increase its profits by selling more cars?

Sam Suffolk is a student in MAT103 at SCCC. Sam has data from a random sample of 20 students that represents how many miles​ (rounded to the nearest whole​ mile) each student lives from the SCCC Ammerman campus. Sam organizes this data in the following frequency distribution table. Look at the table carefully and answer the questions that follow.

Sam made two mistakes when creating the classes for this table. Assuming​ Sam's frequencies are​ correct, despite the errors in the class​ limits, answer each of the following.

​Note: The first two lower class limits are correct.

​(a) Identify​ Sam's mistakes.

​(b) Can we determine how many students live 10 miles from the​ campus? If​ so, how​ many? If​ not, why​ not?

​(c) Give an estimate of the number of students in the sample that live more than 25 miles from the campus. If more than one frequency is​ possible, state all possible values.