MAS 201 Zohar

Exam 1 Extra Practice Problems Chapters 1-4

Chapter 1:

1. The following shows the temperatures (high, low) and weather conditions in a given Sunday for some

selected world cities. For the weather conditions, the following notations are used: c = clear; cl =

cloudy; sh = showers; pc = partly cloudy.

City Hi Lo Condition

Acapulco 99 77 pc

Bangkok 92 78 pc

Mexico City 77 57 sh

Montreal 72 56 pc

Paris 77 58 c

Rome 88 68 cl

Toronto 78 61 c

a. How many elements are in this data set?

b. How many variables are in this data set?

c. How many observations are in this data set?

d. Name the variables and indicate whether they are categorical or quantitative.

e. For which variables are arithmetic operations appropriate and for which are they not

appropriate?

2. The following table shows the starting salaries of a sample of recent business graduates.

Income (In $1,000s) Number of Graduates

15 - 19 40

20 - 24 60

25 - 29 80

30 - 34 18

35 - 39 2

a. What percentage of graduates in the sample had starting salaries of at least $30,000?

b. Of the graduates in the sample, what percentage had starting salaries of less than $25,000?

c. Based on this sample, what percentage of all business graduates do you estimate to have

starting salaries of at least $20,000?

Chapter 2:

3. A student has completed 20 courses in the School of Arts and Sciences. Her grades in the 20 courses

are shown below.

A B A B C

C C B B B

B A B B B

C B C B A

a. Develop a frequency distribution and a bar graph for her grades.

b. Develop a relative frequency distribution for her grades.

4. Below you are given the examination scores of 20 students.

52 99 92 86 84

63 72 76 95 88

92 58 65 79 80

90 75 74 56 99

a. Construct a frequency distribution for this data. Use a class width of 10 and give the first

class a lower limit of 50.

b. Construct a cumulative frequency distribution.

c. Construct a relative frequency distribution.

d. Construct a cumulative relative frequency distribution.

5. The SAT scores of a sample of business school students and their genders are shown below.

SAT Scores

Gender Less than 20 20 up to 25 25 and more Total Female 24 168 48 240

Male 40 96 24 160

Total 64 264 72 400

a. How many students scored less than 20?

b. How many students were female?

c. Of the male students, how many scored 25 or more?

d. Compute row percentages.

e. Compute column percentages.

6. A sample of the ages of 10 employees of a company is shown below.

20 30 40 30 50

30 20 30 20 40

Construct a dot plot for the above data.

Chapter 3:

7. In 2005, the average age of students at UTC was 22 with a standard deviation of 3.96. In 2006, the

average age was 24 with a standard deviation of 4.08. In which year do the ages show a more

dispersed distribution? Show your complete work and support your answer.

8. The following data show the yearly salaries of football coaches at some state supported universities.

Salary

University (in $1,000) A 53

B 44

C 68

D 47

E 62

F 59

G 53

H 94

For the above sample, determine the following measures.

a. The mean yearly salary

b. The standard deviation

c. The mode

d. The median

e.

f.

g.

The 70th percentile, and interpret the meaning.

Was University H an outlier by IQR definition?

Was University H an outlier by z-score definition?

9. The following observations are given for two variables.

y x 5 2

8 12

18 3

20 6

22 11

30 19

10 18

7 9

a. Compute and interpret the sample covariance for the above data.

b. Compute the standard deviation for x.

c. Compute the standard deviation for y.

d.

e.

Compute and interpret the sample correlation coefficient.

Sketch a scatter diagram for the data set.

10. The standard deviation of a sample was reported to be 7. The report indicated that =

980. What was the sample size?

Chapter 4:

11. A college plans to interview 8 students for possible offer of graduate assistantships. The college has

three assistantships available. How many groups of three can the college select?

12. From a group of seven finalists to a contest, three individuals are to be selected for the first and

second and third places. Determine the number of possible selections.

13. Assume you have applied for two scholarships, a Merit scholarship (M) and an Athletic scholarship

(A). The probability that you receive an Athletic scholarship is 0.18. The probability of receiving

both scholarships is 0.11. The probability of getting at least one of the scholarships is 0.3.

a. What is the probability that you will receive a Merit scholarship?

b. Are events A and M mutually exclusive? Why or why not? Explain.

c. Are the two events A, and M, independent? Explain, using probabilities.

d. What is the probability of receiving the Athletic scholarship given that you have been

awarded the Merit scholarship?

e. What is the probability of receiving the Merit scholarship given that you have been awarded

the Athletic scholarship?

14. An experiment consists of throwing two six-sided dice and observing the number of spots on the

upper faces. Determine the probability that

a. the sum of the spots is 3.

b. each die shows four or more spots.

c. the sum of the spots is not 3.

d. neither a one nor a six appear on each die.

e. a pair of sixes appear.

f. the sum of the spots is 7.

15. Assume two events A and B are mutually exclusive and, furthermore, P(A) = 0.2 and P(B) = 0.4.

a. Find P(A B). b. Find P(A B). c. Find P(A B).

16. You are given the following information on Events A, B, C, and D.

P(A) = .4 P(A D) = .6 P(B) = .2 P(AB) = .3 P(C) = .1 P(A C) = .04 P(A D) = .03

a. Compute P(D).

b. Compute P(A B). c. Compute P(AC). d. Compute the probability of the complement of C.

e. Are A and B mutually exclusive? Explain your answer.

f. Are A and B independent? Explain your answer.

g. Are A and C mutually exclusive? Explain your answer.

h. Are A and C independent? Explain your answer.

17. The following table shows the number of students in three different degree programs and whether

they are graduate or undergraduate students:

Undergraduate Graduate Total

Business 150 50 200

Engineering 150 25 175

Arts & Sciences 100 25 125

Total 400 100 500

a. What is the probability that a randomly selected student is an undergraduate?

b. What percentage of students is engineering majors?

c. If we know that a selected student is an undergraduate, what is the probability that he or she

is a business major?

d. A student is enrolled in the Arts and Sciences school. What is the probability that the student

is an undergraduate student?

e. What is the probability that a randomly selected student is a graduate Business major?

18. Assume a businessman has 7 suits and 8 ties. He is planning to take 3 suits and 2 ties with him on

his next business trip. How many possibilities of selection does he have?

19. The results of a survey of 800 married couples and the number of children they had is shown below.

Number of Children Probability 0 0.050

1 0.125

2 0.600

3 0.150

4 0.050

5 0.025

If a couple is selected at random, what is the probability that the couple will have

a. Less than 4 children?

b. More than 2 children?

c. Either 2 or 3 children?

Exam 1 Extra Practice Solutions Chapters 1-4

1. a. 7

b. 3

c. 7

d. Hi: quantitative, Lo: quantitative, Condition: categorical

e. Hi: appropriate, Lo: appropriate, Condition: not appropriate

2. a. 10%

b. 50%

c. 80%

3. Grade Frequency Relative Frequency

A 4 0.20

B 11 0.55

C 5 0.25

Total: 20 1.00

4. a. b. c. d.

Cumulative Cumulative Relative Relative

Score Frequency Frequency Frequency Frequency 50 - 59 3 3 0.15 0.15

60 - 69 2 5 0.10 0.25

70 - 79 5 10 0.25 0.50

80 - 89 4 14 0.20 0.70

90 - 99 6 20 0.30 1.00

Total 20 1.00

5. a. 64

b. 240

c. 24

5d. SAT Scores Gender Less than 20 20 up to 25 25 and more Total Female 10% 70% 20% 100%

Male 25% 60% 15% 100%

e. SAT Scores Gender Less than 20 20 up to 25 25 and more

Female 37.5% 63.6% 66.7%

Male 62.5% 36.4% 33.3%

Total 100% 100% 100%

6.

10 20 30 40 50 60

7. Coefficient of Variation for 2005 = 18%,

Coefficient of Variation for 2006 = 17%

Therefore 2005 shows a slightly more dispersed distribution.

8.

a. 60

b. 15.8

c. 53

d. 56

e.

f.

g.

62 At least 70% of the data is < or = to 62 and at least 30% is > or = to 62. The upper limit is 87.5, so yes, University H was an outlier by IQR definition.

Hs z-score was approximately 2.15, so it would not be considered an outlier by the z-score definition.

9.

a. 19.286 (rounded). Since the covariance is positive, it indicates a positive relationship

between x and y. Larger xs tended to go with larger ys and smaller xs tended to go with smaller ys.

b. 6.32

c. 8.83

d. 0.345. There is a positive linear relationship between x and y. The linearity of the

relationship is not very strong. Meaning that a linear function is not the best model to

represent this relationship.

10. 21 11. 56 12. 210

13.

a. 0.23

b. No, because P(A M) 0 c. No, because P(A M) P(A) P(M) d. 0.4783

e. 0.6111 4.

14.

15.

a. 2/36

b. 9/36

c. 34/36

d. 16/36

e. 1/36

f. 6/36

a. 0.0

b. 0.6

c. 0.0

16.

a.

0.23

b. 0.06

c. 0.4

d. 0.9

e. No, P(A B) 0 f. No, P(A B) P(A) g. No, P(A C) 0 h. Yes, P(A C) = P(A)

17. a. 0.8

b. 35%

c. 0.375

d. 0.8

e. 0.1

18. 980

19.

a. 0.925

b. 0.225

c. 0.75

EXAM 1 FORMULA SHEET

CHAPTERS 3 and 4

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