Back to AIMS Resource Page  Back to AIMS Math Preparatory Materials
 Back to AIMS Math Materials Resource Page  

 

STANDARD 2
DATA ANALYSIS AND PROBABILITY

(Grades 9 - 12)

Vocabulary

biased experimental probability interval permutation scattergram unbiased
box and whisker extrapolate mean population skew variance
central tendency frequency median positive correlation standard deviation
combination histogram mode probability stem and leaf
data independent events negative correlation random success
dependent events inner quartile range outcome range symmetry
event interpolate outlier sample theoretical probability

Read here before you begin

Problems

The following are students’ scores achieved on a math test: 80, 65, 75, 90, 50, 60, 85, 80, 90, 100, 80, 70, 25, 50, 85, 70, 60, 75, 80, 65, 85.

A. Frequency Table

Scores

25

30

35

40

45

50

55

60

65

70

75

80

85

90

95

100

Number Achieved

1

0

0

0

0

2

0

2

2

2

2

4

3

2

0

1

B. Histogram

C. Box and Whisker

 

 D. Stem and Leaf Plot

2 5
3
4
5 0 0
6 0 0 5 5
7 0 0 5 5
8 0 0 0 0 5 5 5
9 0 0
10 0

 

1) Which of the above representations is incorrect?

a) Frequency Table
b) Histogram
c) Box and Whisker Plot
d) Stem and Leaf Plot

 Answer

2) Using figure C above, which observation is an outlier?

a) 25
b) 75
c) 100
d) 50

Answer

3) Using the following three choices; determine which is the correct inference for the above data?

I. The distribution is skewed.
II. The distribution is normal
III. The distribution is symmetric.

a) I
b) II and III
c) III
d) none of the above

Answer

4) The organization of Big-Bucks Inc. is presented below. It shows the number of employees in each position and their corresponding annual salary.

Number of employees 10 5 8 4 1
Salary 22,000 32,500 36,600 49,500 200,000

Which salary skews the data and if removed would make the mean and median approximately equal?

a) 22,000
b) 49,000
c) 200,000
d) 36,600

  Answer

This table represents the income of various professionals based on their number of years of education

Years of Education (x)

8

10

12

12

13

14

16

16

18

19

Income in $1,000 (y)

13

14

17

17.5

20.6

21

24

25

30

31

 

5) Determine a possible equation of the line of best fit for the above data.

Answer

6) Predict the income of a person with 15 years of education.

a) 35.0 b) 14.3
c) 31.4 d) 22.8

Answer

7) Which equation best models the following data?

X

0

1

2

3

4

Y

2

3.2

5.7

10.8

18.2

 

a) y = 3/2x + 2 b) y = - x2 + 2 c) y = x2 + 2 d) y = 4x + 2

Answer

8) You are determining how many people at your school like cafeteria food. You ask only the students in line to purchase cafeteria food. This is an example of a(n):

a) Biased sample b) Unbiased sample c) Random sample d) Census

 Answer

9) The results of the 1996 presidential election indicated that 43% voted for Clinton, 38% for Bush and 19% for Perot. Suppose you randomly sample 150 voters, what number of voters in this sample would you expect would have voted for Bush?

a) 38
b) 76
c) 57
d) 43

Answer

10) The hypothesis is that 45% of the M & M’s manufactured are blue. Which of the following is a valid design for a statistical experiment?

a) Pick 12 M&M’s and determine the number of blue candies.
b) Randomly select 10 bags and count all the M&M’s to determine the number of blue candies.
c) Poll your class of 25 students and ask them what percent they think are blue.
d) Acknowledge that all colors are equally likely and therefore occur in the same percentage.

Answer

11) A fair coin is flipped 100 times and it comes up tails 43 times. Using theoretical probability, what would you expect the number of tails to be if you flipped a coin 1000 times?

a) 430
b) 500
c) 43
d) 570

Answer

12) If the experts indicate that 490 people out of a town of 3500 were likely to get the new strain of flu, what would be the probability that you would get the flu if you lived in that town?

a) 0.10
b) 0.14
c) 0.35
d) 7.14

Answer

13) A bag has 6 red, 4 blue and 8 white marbles. What is the probability of drawing a blue marble from the bag?

a) 1/4
b) 2/9
c) 7/9
d) 3/4

Answer

14) A bag has 6 red, 4 blue and 8 white marbles. What is the probability of drawing a white marble and then a blue marble, with replacement?

a) 8/81
b) 2/3
c) 16/153
d) 104/153

Answer

15) A bag has 6 red, 4 blue and 8 white marbles. What is the probability of drawing a blue, then a red marble, without replacement?

a) 4/51
b) 2/27
c) 5/9
d) 88/153

 Answer

One student will be chosen randomly from your school to attend a breakfast with some community leaders.

 

Class

 

Boys

 

Girls

 

Freshman

 

150

 

120

 

Sophomore

 

100

 

110

 

Junior

 

115

 

125

 

Senior

 

105

 

100

 

16) Refer to the chart above. What is the probability that the student chosen will be a junior?

a) 115/470 b) 125/455 c) 240/925 d) 470/925

Answer

17) From the chart above what is the probability that the student chosen would be a freshman or a sophomore?

a) 230/250 b) 210/925 c) 270/925 d) 480/925

Answer

18) From the chart above what is the probability that the student chosen would be a senior girl?

a) 100/455 b) 100/925 c) 455/925 d) 205/925

 

This situation applies to the next two problems. You need to model a family with three children. You are to determine the gender makeup using probability. To create your data you toss three fair coins to simulate the gender makeup of a family with 3 children. Let heads represent girls and tails represent boys.

  Answer

19) What is the probability of having one girl and two boys?

a) 1/4
b) 1/8
c) 3/8
d) 1/3

Answer

20) What is the probability that all the children are of one gender?

a) 1/4
b) 1/8
c) 1/2
d) 1/3

Answer

21) Which is not a possible outcome for this tree diagram?

 

a) A B D H
b) A C F J
c) A B E J
d) A C F M

Answer

22) A group of five (5) students needs to be selected out of the seven member student council. How many different groups of five (5) can be selected?

a) 120
b) 2,520
c) 21
d) 42

Answer

23) A music group has six songs to select from to create a four song mini-compact disc (CD). How many different ways can the CD be recorded?

a) 256
b) 15
c) 360
d) 24

Answer

24) Which histogram below represents the distribution of possible outcomes for 100 tosses of 12 fair coins if all twelve coins are tossed simultaneously?  In the following graphs, the first column is 0 heads, the second is 1 head,.... and the last is 12 heads.  

 

a.

(# Heads is per toss of all 12 coins)

 

b.

(# Heads is per toss of all 12 coins)

c.

(# Heads is per toss of all 12 coins)

d.

(# Heads is per toss of all 12 coins)

Answer

25) Choose the mean (m ) and standard deviation (s ) that best fits the data from the normal curve below.


Seconds

 

a) m = 80, s = 20
b)
m = 80, s = 60
c)
m = 60, s = 40
d)
m = 80, s = 120

Answer

26) The bell shaped curve above represents the distribution of time it takes children to solve/assemble a certain puzzle. What is the probability it will take a child between 60 and 100 seconds to solve the puzzle?

a) 0.50
b) 0.68
c) 0.40
d) 0.75

Answer

27) The bell shaped curve above represents the distribution of time it takes children to solve/assemble a certain puzzle. What percent of children will take more than 100 seconds to solve the puzzle?

a) 40 %
b) 16 %
c) 84 %
d) 100 %

Answer

28) You have five coins, two nickels and three dimes. You pick two coins simultaneously. What are all of the possible monetary values you can have?

a) 5, 10, 15
b) 5, 10, 25
c) 10, 15, 20
d) 10, 15, 30

Answer

29) The following data: mean = 76, median = 80, mode = 62 and range is 40 to 100, was computed from the test scores of 33 students of Ms. Adams’ algebra class. Using the information determine which statement is true.

a) The lowest score was 36.
b) The grade that was scored most often was 80.
c) Half of the students scored over 76.
d) At least seventeen (17) students scored 80 or below.

Answer

30) The following scatter plots represent the number of chocolate chips in a selected group of cookies from two manufacturers: Company A and Company B. Determine which is true; assuming the scale is the same on both graphs.

 

COMPANY A

COMPANY B

{Vertical (y) axis - # of cookies, horizontal (x) axis = # of chips}

a) Your chance of getting more chocolate chips in your cookie is significantly greater with Company A.
b) Your chance of getting exactly 11 chocolate chips in your cookie is greater with Company A.
c) It is safe to assume that Company A uses significantly more chocolate chips than Company B.
d) You are much more likely to get a wider variance in the number of chocolate chips from Company A.

Answer

31) Which scatter plot represents a strong negative correlation?

a)

b)

c)

d)

Answer

32) Rincon High School’s varsity wrestling team has thirteen (13) wrestlers with a mean weight of 153 lbs. and a median of 158 lbs. What weight of one of the thirteen do we know for sure?

a) 153 c) 158
b) 160 d) 155

Answer

33) On a math test given to a 4th period algebra class at THMS the following scores were earned: 75, 82, 93, 72, 65, 78, 87, 91, 75, 83, 77, 69, 86, 90, 99, 73, 79, 80, 81. Create a frequency table to reflect the given information.

 

 

 

 

Answer

34) The triangular pattern of numbers below is part of the arrangement called Pascal’s Triangle:

 

1 Row 0
1 1

1

1 2 1

2

1 3 3 1

3

1 4 6 4 1

4

1 5 10 10 5 1

5

__ __ __ __ __ __ __

6

Look for a pattern and then fill in the blanks to complete row 6.

Answer

35) How many different lunches are possible when choosing from a menu that includes

3 sandwiches (ham, salami, or bologna),
3 soups (onion, chicken noodle, and vegetable)
3 beverages (milk, juice, or iced tea)?

a) 9 c) 3
b) 27 d) 15

Answer

36) This data represents the number of hamburgers sold each day for one month in Palo Verde’s cafeteria.

98 86 112 94 133 89 138 111
102 124 130 126 94 105 93 107
114 126 83 104 137 122 100 135
135 132 101 116 121 136 108  

What numbers would you use for the stems of a stem-and-leaf plot of this data?

a) 4 through 6 c) 1 through 9
b) 8 through 13 d) 4 through 14

Answer

37) One bag contains 3 red, 2 white, and 5 green marbles. Another bag contains 4 white, 5 red and 2 blue blocks. A marble and a block are drawn from the bags without looking, What is the probability of drawing a green marble and red block?

a) 25 b) 3/4 c) 105/110 d) 5/22

 Answer

38) Pizza Hut offers a special pizza with 4 toppings. There are 11 Toppings available to choose from. Guido decides to order a different 4-topping pizza every day. How many days can Guido go without repeating?

a) 1,663,200 days c) 7,920 days
b) 330 days d) 69,300 days

Answer

39) Using the following information, find the taxable income for a married couple with three exemptions and an adjusted gross income of $24,044.

 Standard Deduction  Personal Exemptions
 $3,100 for single taxpayers  $2,000 for each exemption claimed
 $5,200 for married couples
 $4,550 for heads of households
a) $24,044 c) $16,844
b) $18,844 d) $12,844

Answer

40) Bob’s scores on 4 science tests are 76, 95, 94, and 85. What score must he get on the fifth test to have a 85 average?

a) 72 c) 80
b) 70 d) 75

Answer

41) You have two spinners. One has possible outcomes of { 1, 2, 3, 4, 5, 6 } the other has possible outcomes of { 1, 2, 3, 4, 5 }. The chart below represents all of the equally likely outcomes when both spinners are spun.

 If both spinners are spun, what is the probability that the sum will be less than five?

a) 1/5 b) 2/15 c) 4/5 d) 7/30

Answer

42) Two people are attending a movie theater complex that is showing three different movies. If they are choosing independently what is the best tool and technique to demonstrate the chance that they will attend the same movie.

a) flipping two coins
b) one spin of a three choice wheel
c) throwing a cube with faces labeled { 1, 1, 2, 2, 3, 3 } twice.
d) flipping two coins twice.

Answer

43) A person has two sock drawers organized as follows:

drawer 1: white socks & blue socks
drawer 2: red socks, black socks, & yellow socks

 Which of the following statements is true?

a) From drawer 1: drawing a white sock and then drawing a second white sock are independent events.
b) From drawer 1: drawing a white sock replacing it and then drawing a blue sock are independent events
c) Drawing a blue sock from drawer 1 and then drawing a black sock from drawer 2 are dependent events
d) From drawer 2: drawing a red sock replacing it and then drawing a yellow sock are dependent events.

Answer

44) The graph on the right best reflects which set of living expenses?

a) food $1000, housing $500, utilities $250, misc. $250

b) food $250, housing $25, utilities $500, misc. $1000

c) food $500, housing $1000, utilities $250, misc. $250

d) food $500, housing $250, utilities $1000, misc. $250

Answer

45) Fifty of the two hundred voters at a polling site can best be described as:

a) population c) event
b) sample d) none of the above

Answer

46) Jimmy has a bank card that has a four digit pin number. Any of the four digits in the number may be any number from zero to nine. How many possible combinations are there for that pin number?

a) 20
b) 400
c) 1,000
d) 10,000

Answer

47) A bank vault has a secret code. If the code has two letters followed by four digits, how many combinations are possible?

a) 20
b) 6,000
c) 6,760,000
d) 2,400,000,000

 Answer

Given the following numbers: 72, 73, 80, 78, 72 find the following:

48) the median 49) the mode 50) the mean
a) 80 a) 75 a) 75
b) 73 b) 80 b) 81
c) 75 c) 72 c) 78
d) 25 d) 4 d) 82

Answer                                      Answer                          Answer

 

 

The spinner above is divided into 4 equal parts, and one of those parts is divided into three parts. Use the spinner to answer the following questions.

51) What is the probability of landing in the red area?

a) 25%
b) 50%
c) 75%
d) 32.4%

Answer

52) What is the probability of landing in the brown area?

a) 1/12
b) 1/16
c) 1/3
d) 1/4

Answer

53) What is the probability of landing in the black area?

a) 1.00
b) .50
c) .35
d) 2.00

Answer

54) What is the probability of the spinner landing on a six?

a)

b)

c)

d)

 Answer

55) A die has the numbers 2,3,5,7,9,13. If the die is tossed once, what is the probability of rolling an even number?

a) 1/13
b) 2/13
c) 0
d) 1/6

Answer


Back to AIMS Resource Page  Back to AIMS Math Preparatory Materials
 Back to AIMS Math Materials Resource Page  

Copyright 2000 Tucson Unified School District/Department of Planning & Assessment. All rights reserved.