Mfe 6000 - what is the probability a student will pass the

Question

Question 1. Assume that there are four groups of employees in a company. The annual income of each group is as follows:
Group A: $60,000
Group B: 55,000
Group C: 52,000
Group D: 48,000

Assume further that there are 10 employees in group A, 20 in group B, 25 in group C, and 35 in group D. Calculate the weighted average.

Question 2. The table below gives the annual total returns on Global Balanced Index Fund from 1999 to 2008. The returns are in the local currency. Use the information in this table to answer the following questions:

Table 1: Global Balanced Index Fund Total Returns, 1999-2008

Year	Return
1999	50.21%
2000	-2.18%
2001	12.04%
2002	26.87%
2003	49.90%
2004	24.32%
2005	45.20%
2006	-5.53%
2007	-13.75%
2008	-39.06%

a. Calculate the mean absolute deviation (MAD).

Calculation of MAD for Germany Index Total Returns, 1999-2008
Year	Return
1999	50.21%
2000	-2.18%
2001	12.04%
2002	26.87%
2003	49.90%
2004	24.32%
2005	45.20%
2006	-5.53%
2007	-13.75%
2008	-39.06%

b. Calculate the variance.

Calculation of Variance for Germany Index Total Returns, 1999-2008
Year	Return
1993	46.21%
1994	-6.18%
1995	8.04%
1996	22.87%
1997	45.90%
1998	20.32%
1999	41.20%
2000	-9.53%
2001	-17.75%
2002	-43.06%

c. Calculate the standard deviation.

c. Calculate the semi variance (the average squared deviation below the mean), a measure of downward risk.

Question 3. According to the "January theory," if the stock market is up for the month of January, it will be up for the year. If it is down in January, it will be down for the year. According to an article in the Wall Street Journal, this theory held for 29 out of the last 34 years. What is the probability that this will happen exactly 29 times in a sample 40 years?

That is, if this process repeats itself many times, what is the probability of having a bull market 29 out of 40 years?

Question 4. Suppose the mean and the standard deviation of a distribution are as follows: population mean and standards deviation are 60 and 5, respectively. At least what proportion of the observations lie between 45 and 75?

Question 5. We have collected data for two distributions and calculated the following two statistics:
X‾_A = 10, s_A = 5,
X‾_B = 50, s_B = 20 ,
Can we conclude that distribution B is more dispersed than distribution A?

Question 6. The table below gives statistics relating to a hypothetical 10-year record of two portfolios.

	Mean Annual Return (%)	Standard Deviation of Return (%)	Skewness
Portfolio A	10.25	23.4	-3.4
Portfolio B	10.25	19.5	4.5

Based only on the information in the above table, perform the following:

A. Contrast the distributions of returns of Portfolio A and B.

B. Evaluate the relative attractiveness of Portfolios A and B.

Question 7. An analyst gathered the following information:

Portfolio	Mean Return(%)	Standard Deviation of Returns(%)
1	9.8	19.9
2	10.5	20.3
3	13.3	33.9

If the risk-free rate of return is 3.0 percent, the portfolio that had the best risk-adjusted performance based on the Sharpe ratio is: (explain why)
A. Portfolio 1.
B. Portfolio 2.
C. Portfolio 3.

Question 8. A survey of undergraduate students in the School of Business at Northern University revealed the following regarding the gender and majors of the students:

		Major
Gender	Accounting	Management	Finance	Total
Male	100	150	50	300
Female	100	50	50	200
Total	200	200	100	500

a. What is the probability of selecting a female student?

b. What is the probability of selecting a finance or accounting major?

c. What is the probability of selecting a female or an accounting major?

d. What is the probability of selecting a male accounting major?

e. What is the probability of selecting a male student given that the student is majoring in accounting?

f. Let A denote the event that a student is a male and B denote the event that the student is majoring in finance. Are event A and B independent?

Question 9. A portfolio is 50% invested in an S&P 500 index fund, 25% invested in a U.S. long-term corporate bond fund, and 25% invested in an Exchange Traded Funds (ETF). Suppose we have estimated expected returns on the assets in the portfolio. Table 1 shows these weights and the expected return on the individual assets and Table 2 shows the variance covariance matrix:

Table 1: Portfolio weights and Expected Returns

Asset Class	Weight	Expected Return (%)
S&P 500 Index	0.5	13
Corporate Long-Term Bond	0.25	6
Exchange Traded Funds (ETFs)	0.25	15

Table 2: Portfolio Covariance Matrix

	S&P 500 Index	Corporate Long Term Bonds	Exchange Traded Funds
S&P 500 Index	400	45	189
Corporate Long-Terms Bonds	45	81	38
Exchange Traded Funds (ETFs)	189	38	441

a. Calculate the expected return on the portfolio.

b. Calculate the portfolio variance and standard deviation.

Question 10. Compare the standard normal distribution and Student's t-distribution.

Question 11. The portfolio mean return estimate was 8 percent and the standard deviation of return estimate was 10 percent per year. Assuming that a normal distribution describes returns, answer the following questions:

a. What is the probability that portfolio returns will exceed 15%?

b. What is the probability that portfolio returns will be below 5%?

Question 12. An investment will be worth $1,000, $2,000, or $5,000 at the end of the year. The probabilities of these values are 0.25, 0.60, and 0.15, respectively. Determine the mean and variance, and the standard deviation of the worth of investment.

Question 13. In a recent survey in a Statistics class, it was determined that only 60% of the students attend class on Thursday. From past data it was noted that 98% of those who went to class on Thursday pass the course, while only 20% of those who did not go to class on Thursday passed the course.

Let:
A1: the students attend class on Thursday
A2: the students do not attend class on Thursday
B1: the students pass the course
B2: the students do not pass the course

(a) What is the probability a student will pass the course?

(b) Given that a student passes the course, what is the probability that he/she attended classes on Thursday.

Question 14. The Georgetown, South Carolina, Traffic Division reported 40% of the high-speed chases involving automobiles result in a minor or major accident. During a month in which 150 high-speed chases occur, what is the probability that 50 or more will result in a minor or major accident?

Question 15. The braking system on a certain car will stop it in a mean distance of 60 feet when traveling 35 miles per hour. A new system, thought to be superior, has been developed. The new system is installed on 36 cars and the mean stopping distance is 56 feet, with a sample standard deviation of 7 feet. At α = 0.01 can we conclude that the new system will stop the car faster?

Question 16. A study of the health benefits packages for employees of large and small firms was recently completed by Pohman Associates, a management consulting firm. Among the 15 large firms studied, the mean cost of the benefits package was 17.6 percent of salary, with a standard deviation of 2.6 percent. Among the 12 small firms studied, the mean cost of the benefits package was 16.2 percent of salary, with a standard deviation of 3.3 percent. Is there a significant difference between the mean percent of the employees' salaries spent by large firms and by small firms on health benefits? Use the 0.05 level of significance.

Question 17. Kameran Associates is a marketing research firm that specializes in comparative shopping. Kamran is hired by Ford to compare the selling price which is obtained after the usual bargaining process at the Fusion Hybrid and Ford Focus dealerships. Posing as a potential customer, a representative of Kamran visited 8 Fusion Hybrid dealerships and 6 Ford Focus dealerships in Metro City and obtained quotes on these two cars. The standard deviation for the selling price of 8 Fusion Hybrid dealerships is $350 and that for the 6 Ford Focus dealerships is $290. At the 0.01significance level, can we conclude that there is more variation in the quotes of Fusion Hybrid?