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__STANDARD 2DATA 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 |

**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 ½ 5 3 ½ 4 ½ 5 ½ 0 0 6 ½ 0 0 5 5 7 ½ 0 0 5 5 8 ½ 0 0 0 0 5 5 5 9 ½ 0 0 10 ½ 0

**1)** Which of the above representations is
incorrect?

a) Frequency Table

b) Histogram

c) Box and Whisker Plot

d) Stem and Leaf Plot

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

a) 25

b) 75

c) 100

d) 50

**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

**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

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.

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

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

**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 = - x^{2} + 2 |
c) y = x^{2} + 2 |
d) y = 4x + 2 |

**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

**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

**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.

**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

**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

**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

**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

**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) 88/153One student will be chosen randomly from your school to attend a breakfast with some community leaders.

Class

Boys

Girls

Freshman150

120

Sophomore100

110

Junior115

125

Senior105

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

**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

**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.

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

a) 1/4

b) 1/8

c) 3/8

d) 1/3

**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

**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

**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

**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

**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) |

**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

**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

**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 %

**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

**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.

**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.

**31) **Which scatter plot represents a strong negative
correlation?

a) |
b) |

c) |
d) |

**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

**33) **On a math test given to a 4^{th} 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.

**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.

**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

**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

**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

**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

**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

**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

**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

**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.

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

drawer 1: white socks & blue socks

drawer 2: red socks, black socks, & yellow socksWhich 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.

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

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

**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

**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

**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

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 |

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%

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

a) 1/12

b) 1/16

c) 1/3

d) 1/4

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

a) 1.00

b) .50

c) .35

d) 2.00

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

a)

b)

c)

d)

**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

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