You may use the extra sheets of paper to solve the following questions, but please report your results and conclusions in the space provided.  Whenever possible, show your work for potential partial credit.  NOTE:  When performing numerical calculations, keep at least 4 digits after a decimal.  (I.e., do NOT round .2265 to .23 or .227)  BUDGET YOUR TIME WISELY!

1.  The following data set provides information about five college professors.

Name

Zip Code

Years of Experience

Married (Y=1, N=0)

Annual Salary $

Academic Discipline

Kip

47243

28

1

125,000

Economics

Kendra

20012

2

1

33,000

Marketing

Jessica

97042

15

1

89,000

Finance

Ryan

45467

1

0

31,500

European History

Rick

97224

1

0

28,500

Statistics

a.  How many elements, variables and observations are in this data set?  (3 points)

 

 

b.  Which of the variables are in this data set are qualitative and which are quantitative?  Explain.  (5 points)

 

 

 

 

 

 

2.  The following data elements represent the amount of time (rounded to the nearest second) that 30 randomly selected customers spent in line before being served at a branch of River View Financial Bank.

183

121

140

198

199

90

62

135

60

175

320

110

185

85

172

235

250

242

193

75

263

295

146

160

210

165

179

359

220

170

a.  Develop a frequency, relative frequency, and cumulative frequency distribution for the above data.  (9 points)

b.  Use your table to provide your boss with two specific statistical inferences to summarize the time spent in line at the bank.  (6 points)

3.  The table below provides you with the U.S. annual unemployment rate (UR) and rate of consumer price inflation (I) for each of the last 8 years.

Year

Unemployment

Rate

Inflation

1997

4.9%

2.29%

1998

4.5%

1.56%

1999

4.2%

2.21%

2000

4.0%

3.36%

2001

4.7%

2.85%

2002

5.8%

1.58%

2003

6.0%

2.28%

2004

5.5%

2.61%

a.  Calculate the mean and median of both UR and I.  Carefully interpret these values.  (4 points)

 

 

 

 

 

 

b.  Calculate the standard deviation for UR.  The standard deviation for I is .6073. Carefully interpret these values.  Which of these economic indicators exhibits more relative variability?  Explain.  (8 points)

 

 

 

 

 

 

 

 

 

 

 

c.  The sample covariance between UR and I is –.00172.  Calculate the correlation coefficient between UR and I.  Carefully interpret both of these values.  Do they make economic sense?  Explain.  (8 points)

 

 

 

 

 

 

 

 

d.  Use the Empirical Rule to determine specific values of I that would include approximately 95% of all values of I?  How would you use the Empirical Rule to investigate outliers in any data set?  Explain.  (8 points)

4.  Sue is a general contractor and has submitted two bids for two projects (X and Y).  The probability of getting project X is .65.  The probability of getting project Y is .77.  The probability of getting at least one of the two projects is .90.  What is the probability of getting both projects?  Are the events of getting both projects mutually exclusive?  Explain using probabilities and intuitively explain your responses.  (6 points)

 

 

 

 

 

 

 

 

 

 

5.  During the registration period at a local college, students consult their advisors about course selection.  A particular advisor noted that during each half hour an average of 5 students came to see her for advising. 

a. What is the probability that fewer than 3 students will consult with her in a 30-minute period?  (3 points)

 

 

 

 

 

 

b.  The advisor does not yet have tenure at the local college.  If she is not in her office when a student stops by for advising, she will receive a nasty letter in her personnel file, and this could mean that she does not receive tenure next year.  But if the professor does not go to the bank, to deposit some money, an errand of 12 minutes, her rent check will bounce. The professor calls you to ask your advice.  Give it, being careful to explain your reasoning.  (6 points)

 

 

 

 

 

 

 

 

6.  A local university reports that 5% of their students take their general education courses on a pass/fail basis.  Assume that 30 students are registered for a general education course. 

a.  What is the expected number of students who have registered on a pass/fail basis?  (2 points)

 

 

b.  What is the probability that exactly three are registered on a pass/fail basis?  (2 points)

 

 

 

 

c.  What is the probability that at least 2 are registered on a pass/fail basis?  (4 points)

 

 

 

 

 

 

7.  A statistics survey has tried to measure the relationship between drug use and drinking.  The event A is that a student claims to drink alcohol at least once in a typical week.  The event D is that a student has tried illegal drugs at least once.

a.  Complete the table by filling in the missing values.  (3 points)

 

A

Ac

Totals

D

 

 

44

Dc

 

18

 

Totals

64

 

85

b.  Calculate the conditional probability of drinking given drug use and the conditional probability of drug use given drinking.  (4 points)

 

 

 

 

 

c.  What do these conditional probabilities tell you about the connection between these two events?  Which event do you suppose is a better predictor of the other event?  Discuss independence between the two events.  (10 points)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

8.  Discuss the role of independence in all three of the discrete probability distributions discussed in class this semester .  Feel free to use examples if necessary.  (9 points)