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OPRE-202 – Mid-Term Exam
General Instructions
• There are 10 Multiple choice (10 points) and 5 Problems (5×10=50 points) for
a total of 60 points
• Submission: There are multiple ways to Submit the Exam
o Due date for this exam is Monday April 1st by 11 PM (No exceptions)
o Print this document – Hand-write answers , scan and attach as 1 PDFDocument. Show formulas and steps clearly
o Answer all questions in an EXCEL workbook. Please use one tab per
problem. Show Formulas and steps clearly
o You can also use a combination of Word, Hand-written and Excel, but
must combine as 1 PDF document for submission
o There is no TIME-limit on this exam (not a Timed-Test). You have almost
3-days to complete this exam
o Do not take or give help on this test.
o I will not accept any e-mail attachments or SAKAI Message Attachments
Honor Pledge
I, _______________________________, certify that I have completed all
work on my own. Also, I will not discuss any material on the exam with other
students that have yet to take the exam. If it is uncovered that I have not followed
the rules, I can be brought in front of the Honors Code committee.
______________________________________________
Signature
OPRE-202- Intro to STATS – MID-TERM
Total Points: 60
Multiple Choice:(10 Points)
1.
A statistics professor receives an average of five e-mail messages per day from students.
Assume the number of messages approximates a Poisson distribution. What is the probability that on a
randomly selected day she will have five messages?
A.
B.
C.
D.
2.
0.0067
0.8750
0.1755
1.0000
Which one of the following is NOT an example of discrete data?
A.
B.
C.
D.
Number of households watching the Home Shopping Network
Number of employees reporting in sick
Number of miles between New York City and Chicago
Number of members of the Denver Lions Club
3.
The manager of the local grocery store has determined that, on average, 4 customers use the
service desk every half-hour. Assume that the number of customers using the service desk has a Poisson
distribution. What is the probability that during a randomly selected half-hour period, exactly 2 customers use
the service desk?
a .0183
b. .0733
c. .1465
d. .9084
e .7619
4
The time it takes a woman to travel from her apartment to the bus station follows a uniform
distribution over the interval from 20 to 30 minutes. If she leaves home at 9:05 a.m., what is the probability
that she will get to the station between 9:25 and 9:30 a.m.?
5.
A.
1.0
B.
0.0
C.
0.5
D.
0.25
Which of the following is correct about a probability distribution?
A.
B.
c.
d.
The sum of all possible outcomes must equal 1.0.
The outcomes must be mutually exclusive.
The probability of each outcome must be between 0.0 and 1.0 inclusive.
All apply.
6.
A study by the National Park Service revealed that 50% of the vacationers going to the Rocky
Mountain region visit Yellowstone Park, 40% visit the Grand Tetons, and 35% visit both. What is the
probability that a vacationer will visit at least one of these magnificent attractions?
A.
0.95
B.
0.35
C.
0.55
D.
0.05
7.
In a management trainee program, 80% of the trainees are female, while 20% are male. Ninety
percent of the females attended college; 78% of the males attended college. A management trainee is
selected at random. What is the probability that the person selected is a male who did NOT attend college?
A.
0.044
B.
0.440
C.
0.256
D.
0.801
8.
The ABCD football association is considering a Super Ten Football Conference. The top 10
football teams in the country, based on past records, would be members of the Super Ten Conference. Each
team would play every other team in the conference during the season and the team winning the most games
would be declared the national champion. How many games would the conference commissioner have to
schedule each year? (Remember, Oklahoma versus Michigan is the same as Michigan versus Oklahoma.)
A.
45
B.
50
C.
125
D.
14
9.
Chances are 50-50 that a newborn baby will be a girl. For families with five children, what is the
probability that all the children are girls?
10.
A.
0.900
B.
0.031
C.
0.001
D.
0.250
What is the area under the normal curve between z = -1.0 and z = -2.0?
A.
B.
C.
D.
0.0228
0.3413
0.1359
0.4772
Solve the following problems. Show all steps clearly
(5×10=50 points)
1. There are eight flights from Minneapolis to St. Cloud each day. The
probability that any one flight is late is 0.10. Using the binomial probability
formula:
a. what is the probability that none are late?
b. what is the probability that 1 or more are late?
c. what is the probability that exactly 1 flight is late?
d. What is the probability that there are between 3 and 6 flights (both
inclusive) that are late?
2. The mean height of a group of students in a statistics class is 5 ft 6 in and
standard deviation is 2 in. Height is normally distributed. Show Normal
Distribution Sketches in each case.
a. What is the probability that a randomly selected individual is shorter
than 5ft 7 in?
b. What is the probability that a randomly selected individual is taller than
5ft 10 in?
c. What is the probability that a randomly selected individual is between
5ft 3in and 5ft 10in?
d. What height separates the top 25% of the students from the lower 75%
of students?
3 Consider the data in the table
36
46
40
38
39
40
38
38
36
42
33
34
35
34
37
37
36
41
22
17
20
36
33
25
19
42
28
38
a. Find the number of classes needed to construct a histogram. Find the class
length.
b. Draw a frequency histogram for these data.
c. Develop a percent frequency distribution.
d. Also, Plot an OGIVE chart
________________________________________________________________
4. Fifteen percent of the employees in a company have managerial positions, and 25 percent of
the employees in the company have MBA degrees. Also, 60 percent of the managers have MBA
degrees.
a. The Company employs 100 employees. Construct a contingency table.
Show the following with Probability Formulas
b. Find the proportion of employees who are managers and have MBA degrees.
c. Find the proportion of MBAs who are managers.
d. Are the events being a manager and having an MBA independent? Justify your answer.
e. What proportion of the employees are either a manager or have an MBA degree
5. In recent years, due to low interest rates, many homeowners refinanced their home mortgages. Linda
Lahey is a mortgage officer at Down River Federal Savings and Loan. Below is the amount refinanced for 20
loans she processed last week. The data are reported in thousands of dollars and arranged from smallest
to largest.
a.
b.
c.
d.
Find the Mean , Variance, Standard deviation and Range
Find the median, first quartile, and third quartile.
Draw a box plot of the data
Are there any outliers ?
…
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