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

Ed

47243

28

1

125,000

Economics

Beth

20012

2

1

33,000

Marketing

Laura

97042

15

1

89,000

Finance

Tom

45467

1

0

31,500

European History

Margaret

97224

8

0

68,500

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.  (6 points)

b.  The president of the bank asks you to summarize the length of time that customers wait to be served.  Use your table to provide your boss with this information.  Make three specific statistical inferences in your summary.  (9 points)

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

Year

Unemployment

Rate

Consumer Price Index

1994

6.1

148.2

1995

5.6

152.4

1996

5.4

156.9

1997

4.9

160.5

1998

4.5

163.0

1999

4.2

166.6

2000

4.0

172.2

2001

4.8

177.1

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

 

 

 

 

 

 

b.  Calculate the standard deviation for UR.  The standard deviation for CPI is 9.7466. Carefully interpret these values.  Which of these economic indicators exhibits more relative volatility?  Does this make sense?  Explain.  (10 points)

 

 

 

 

 

 

 

 

 

 

 

c.  The covariance between UR and CPI is –5.0217.  Calculate the correlation coefficient between UR and CPI.  Carefully interpret both of these values.  Do they make economic sense?  Explain.  (10 points)

 

 

 

 

 

 

 

 

d.  Use the Empirical Rule to determine what specific values of the CPI would include approximately 95% of all values for the CPI?  How would you use the Empirical Rule to investigate outliers in any data set?  Explain.  (10 points)

4.  Assume you have applied to two different universities (let’s refer to them as A and B) for your graduate work.  In the past, 25% of students (with similar credentials as yours) who applied to University A were accepted; while University B accepted 35% of the applicants.  Assume that acceptance at the two universities are independent events.

a.  What is the probability that you will be accepted to at least one graduate program?  (3 points)

 

 

 

b.  What is the probability that one and only one of the universities will accept you?  (2 points)

 

 

 

 

c.  What is the probability that neither university will accept you?  (2 points)

 

 

 

5.  Tammy 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.  Are the events of getting the two projects mutually exclusive?  Are they independent events?  Explain using probabilities and intuitively explain your responses.  (10 points)

 

 

 

 

 

 

 

 

 

 

 

 

 

6.  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 8 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)

 

7.  A local university reports that 3% of their students take their general education courses on a pass/fail basis.  Assume that fifty 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)

 

 

 

 

 

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