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DEPARTMENT OF MATHEMATICS AND COMPUTER SCIENCE

MATH 2411- INTRODUCTION TO STATISTICS TEST 3 SUMMER 2018

DUE DATE: JUNE 24, 2018

NAME:__Danielle Brown___________________________RamID:____900356044___________

Attempt all questions. Show all your work in the space provided. Good luck.

1. Define the following as related to probability with examples:

(i)

A probability experiment.

(ii)

An outcome.

(iii) A sample space.

(iv)

An event.

(v)

Equally likely events.

(vi)

Independent events.

1

2

2. A bag contains nine red balls, eight white balls, and ten green balls. Suppose two

balls are drawn without replacement.

(a) Draw a tree diagram and present a complete enumeration for the sample space.

(b) Find the probability that:

(i)

All the balls are white.

(ii)

The two balls have distinct colors.

(iii)

At least one ball is red.

(iii)

The two balls are all white or all green.

(iv)

None of the balls is green.

3

3. Generate the sample space obtained by rolling two dice (present this in a tabular

form).

Determine the following:

(a) The probability of obtaining a sum that equals 6.

(b) The probability of obtaining a sum that equal 8.

(c) Probability of obtaining a sum that equals 10 or 11.

(d) The probability of obtaining a sum that equals 9 12 .

4

4(a). A circuit to run a model railroad has 39 switches and 11 are defective. If a person

selects two switches at random and tests them, find the probability that the second one is

defective, given that the first one is defective.

4(b). A flashlight has 43 batteries, 7 of which are defective. If two are selected at random

without replacement, find the probability that both are defective.

5

5.(a) A committee of 8 is to be selected from a 16 men and 12 women. If the committee

has 3 men and five women as members, in how many ways can this be achieved?

(You need not simplify)

5(b) How many different 6-digit identification tags can be made if the digits can be used

more than once? If the first digit must be 9 and repetitions are not allowed?

5 Â©. How many different permutations of the word GONZAGAUNIVERSITY are

there?

6

6. Given the following distribution, perform a Stem and Leaf plot for this data.

65

42

9

28

33

18

12

82

54

90

18

25

6

4

95

77

94

71

34

56

51

41

25

51

87

33

67

53

88

61

72

46

45

61

67

49

79

52

97

77

56

67

43

81

34

10

45

58

94

73

17

74

91

98

8

43

29

19

82

12

22

16

Bonus Question

7. A coin is tossed four times, a die is rolled three times, and three cards are taken from

a pack of 52 cards without replacement. In how many possible ways can this be done?

(You need not expand.

7

DEPARTMENT OF MATHEMATICS AND COMPUTER SCIENCE

MATH 2411- INTRODUCTION TO STATISTICS TEST 4 SUMMER 2018

DUE DATE: JULY 6, 2018

NAME:___Danielle Brown__________________RamID:_900356044________________

Attempt all questions. Answer all the questions in the space provided. Good luck.

1. Determine whether each of the following distributions represents a probability

distribution. If not, state why.

(i)

X

P(X)

20

1.1

30

0.2

40

0.9

50

0.3

(ii)

X

P(X)

1

1

8

3

1

8

5

3

8

1

7

2

8

9

1

8

2. A couple plans to have three children. Assume that one child is born at a time. Let

the random variable X be the number of girls.

(i)

Draw a tree diagram and enumerate all the possible outcomes.

(ii)

Construct the probability distribution for the family of four children.

(ii)

Compute the mean, variance, and standard deviation for this distribution.

2

3. The following distribution shows the number of students enrolled in five English

courses at a local university.

Number of Students

Probability P(X)

28

0.22

35

0.16

41

0.15

43

0.27

(a) Find the mean, variance, and standard deviation for the distribution.

(b) Find the expectation of the enrollment in English classes.

3

48

0.20

4. Zentos Associates Market research found out that 29% of Europeans do not think

having a college education is important to succeed in the business world. If a random

sample of seven Europeans is selected, find these probabilities.

(a)

More than four people will agree with that statement.

(b)

At most three people will agree with that statement.

(c)

At least two people will agree with that statement.

(d)

Nobody agrees with that statement.

(e)

Determine the mean and variance of this distribution.

4

5.(a) State four characteristics of a binomial experiment.

(b) What is a binomial distribution?

Â© Write the expression for the Binomial Distribution function

5

DEPARTMENT OF MATHEMATICS AND COMPUTER SCIENCE

MATH 2411- BASIC STATISTICS TEST 1 SUMMER 2018

DUE DATE : JUNE 8, 2018

NAME: Danielle Brown

RamID 900356044 __

_______

Attempt all questions. Show all your work in the spaces provided. Good luck.

1. Define the following terms as related to statistics with examples.

(i)

(ii)

(iii)

(iv)

(v)

(vi)

(vii)

(viii)

(ix)

Data.

Quantitative variables.

Discrete variable.

Variable.

Probability

Random variable.

Population.

Sample.

Random sample

1

2

2. Below is the list of Test I scores of 75 students in POLS 1111.

65

82

95

51

67

45

100

34

17

29

42

54

77

41

53

61

77

10

74

19

9

90

94

25

88

67

56

45

91

82

28

18

71

51

61

49

67

58

98

12

33

25

34

87

72

79

43

94

8

22

18

6

56

33

46

52

81

73

43

16

12

4

88

74

76

67

29

44

59

72

84

72

9

55

11

(a) Determine the range of the distribution.

(b) Using the class limits 1-10, 11-20, etc, Construction a frequency distribution

indicating the class limits, class boundaries, tally, frequency, and cumulative

frequency.

(c) Construct the histogram associated with this data.

(hint: Use the graph paper below to draw your graph).

3

4

3. Nurses on the sixth floor of a Community Hospital believe that they need more

nurses at night. To estimate the night workload, a random sample of 44 nights was

used. For each night, the total room calls to the nursesâ?? station on the sixth floor was

recorded as follows:

49

90

102

70

68

70

80

87

69

74

86

55

73

46

85

43

83

18

73

72

54

84

86

55

93

82

62

73

86

75

100

77

79

65

90

82

71

101

47

39

92

77

88

66

Using five classes of equal class width, construct a frequency distribution for this

data. (You must include class limits, class boundaries, tally frequency and cumulative

frequency columns as studied in the class).

5

4. 1300 students at Zambezi High School are distributed as follows:

Class

Freshmen

Sophomore

Junior

Senior

(i)

(ii)

(iii)

Number of students

392

337

335

236

Percentage

Complete the given table.

Construct a Bar graph for the data.

Construct a pie graph for this data.

6

Degrees

5. The data below represent of number of billions of bushels of corn produced in the

United States between 2007 and 2017.

Year

Bushels

(in

Billions)

2007

10.1

2008

11.8

2009

11

2010

10.5

2011

13

2012

12.1

2013

13.1

2014

12.5

2015 2017 2017

12.4 11.8 14

Draw a time series graph to represent this data. (Hint: Use two steps on the y-axis to

represent 1 billion bushels, and 3 units on the x-axis to present 1 year).

Is corn production increasing? Give reasons for your answer.

7

6. Below is a sample distribution of exam scores of 17 Calculus 2 students in Test 1 in

the fall of 2009:

65, 42, 77, 25, 11, 89, 92, 44, 54, 17, 65, 77, 14, 88, 65, 33,77.

(a) Find the range of the distribution.

(b) Find the mean, mode and median of the distribution.

8

DEPARTMENT OF MATHEMATICS AND COMPUTER SCIENCE

MATH 2411- INTRODUCTION TO STATISTICS TEST 2

DUE: JUNE 10, 2018

NAME: Danielle Brown

RamID 900356044

.

Attempt all questions in the space provided. Please show all your work. Good luck.

1. The following is a distribution of examination scores of thirty Calculus I students:

65, 88, 81, 94, 97, 35, 13, 49, 67, 72, 74, 19, 66, 37, 56, 77, 79, 14, 29, 72, 77, 45, 77

97, 35, 79, 82, 55, 63, 91

(a) Computer the mean of this distribution.

(b) Determine the mode and the median.

(c) Compute the variance and standard deviation of the data.

(Assume that this is a population distribution).

1

2. The frequency distribution below represents the data obtained from a sample of 90

ATM machine service technicians. The values represent the days service calls for varying

ATM machines.

Class

boundaries

21.5 â?? 25.5

25.5 â?? 29.5

29.5 â?? 33.5

33.5 â?? 37.5

37.5 â?? 41.5

41.5 â?? 45.5

(a)

(b)

(c)

(d)

(e)

(f)

Frequency ( f )

Midpoint X m

f ï?? Xm

13

11

17

22

15

12

Complete the table.

Determine the mean.

Determine the modal class.

Find the median class.

Compute the median.

Find the variance and standard deviation of the distribution.

2

f ï?? X m2

3

3. An aptitude test has a mean of 245 and a standard deviation of 18. Find the

corresponding z â?? score for each examination score.

(i) 281

(ii) 227

(iii) 285

(iv) 222

(v) 255.

4. Given the following data: 54, 67, 32, 88, 178, 62, 15, 45, 19, 37, 11, 69, 49, 17, 72.

(i) Determine Q1 , Q2 , and Q3 .

(ii) Determine the interquartile range (IQR)

(iii) Computer the percentile ranks of 67, 88, and 49.

(iv) Determine an outlier if any.

4

5. Given the following data: 54, 67, 32, 88, 178, 62, 15, 45, 19, 37, 11, 69, 49, 17, 72

(i) Present the associated five-number summary.

(ii) Perform a Box Plot for the data.

5

…

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