Math Solving Problems(1)

Exam 1 - Use your own paper as an answer sheet. Show all mathematical calculations. No partial credit will be given if work is not shown. A calculator will be required to complete the exam. Solving Problems 1. A questionnaire on housing arrangements showed the following information obtained from 30 respondents. Construct a frequency distribution and a pareto chart for the following data. H = house

A = Apartment

M = mobile home

C = condominium

H

C

H

M

C

A

C

A

M

C

M

C

A

M

A

C

C

M

C

C

H

A

H

H

M

C

A

M

A

C

2. When 36 randomly selected customers left a convenience store, each was asked the number of items he or she purchased. Construct a frequency distribution, histogram, and frequency polygon for the data. 2

9

4

3

6

6

6

2

8

6

5

5

7

5

3

8

6

6

6

2

3

2

4

4

6

9

9

8

9

9

4

2

1

7

4

4

3. The temperature of Singing River was recorded at 6 P.M. each day for the month of April. Construct a histogram, and ogive using relative frequencies for the data. Use six classes. 54

53

48

51

49

49

50

53

58

48

42

50

54

53

54

57

56

55

47

48

51

57

55

42

46

43

44

43

47

46

4. The following data represents the expenses of Chemistry Lab, Inc. for research and development for the years indicated. Each number represents millions of dollars. Draw a time series graph to represent the data. Be sure to use the same scale. Year

Amount

1965

$ 8,937

1970

$ 9,388

1975

$ 11, 271

1980

$ 13, 271

1985

$ 19, 203

5. In a study of 100 working teenagers, ages 16-18 the following numbers had given the major reasons for working as shown here. Construct a pie graph for the data. Reason

Number

To buy a car

45

To pay for education

39

For spending money

12

Other

4

6. The following temperatures were recorded in Nevada for a week in April. 87

85

80

78

83

Find each of the following: Must use formulas and show work. a. mean b. median c. mode d. midrange e. range f. variance- must use formula and show work g. standard deviation

86

90

h. z score for a temperature of 85

7. Shown is a frequency distribution for the number of inches of rain received in one year in 25 selected cities in the United States. Number of inches

Frequency

5.5-20.5

2

20.5-35.5

3

35.5-50.5

8

50.5-65.5

6

65.5-80.5

3

80.5-95.5

3

Find each of the following: Must use formulas and show work. a) mean b) median c) modal class d) variance e) standard deviation

8. In a survey of third grade students, the following distribution was obtained for the number of “best friends” each had. Find the average number of “best friends” for the class. Use the weighted mean. Number of students

Number of best friends

8

1

6

2

5

3

3

0

9. A sample of the labor costs per hour to assemble a certain product has a mean of $2.60 and a standard deviation of $0.15. Using Chebyshev’s Theorem, find the values in which at least 88.89% of the data will lie.

10. The number of credits in business courses eight job applicants is shown: 9

12

15

27

33

45

63

72

a) Find the percentile rank for a value of 45 b) What value corresponds to the 40th percentile? c) Construct a box and whisker plot and comment on the nature of the distribution. 11. The number of visitors to the Historic Museum for 27 randomly selected hours is shown below. Construct a stem and leaf plot for the data. 15

53

48

19

38

47

86

63

22

98

79

38

53

62

89

67

39

76

26

41

28

35

54

88

76

68

31