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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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