AnswersTX-Advanced Quantitative ReasoningCumulative Exam

Cumulative Exam — Cumulative exam Answers

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21
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A professor wants to determine information about the Internet usage of middle school students in one state. A sample of 500 boys and girls from middle schools across the state were asked, “How do you access the Internet when you are not at school?” Which best explains why the sample can be used to determine statistics that apply to the population?

A
The sample represents the population.
B
The sample is larger than the population.
C
Each person in the population knows at least one person included in the sample.
D
Each person in the sample has Internet access while they are not at school.
22
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A standard deck of cards has 52 cards, 13 of each of the 4 suits: hearts, diamonds, clubs, and spades. After shuffling the deck, Linbo deals the cards to his friends for the game. Which expression can be used to find the probability that the first three cards that he deals are all hearts if none of them are replaced?

A
(StartFraction 13 over 52 EndFraction) (StartFraction 12 over 52 EndFraction) (StartFraction 11 over 52 EndFraction)
Option A
B
(StartFraction 13 over 52 EndFraction) (StartFraction 12 over 51 EndFraction) (StartFraction 11 over 50 EndFraction)
Option B
C
(StartFraction 13 over 52 EndFraction) (StartFraction 13 over 52 EndFraction) (StartFraction 13 over 52 EndFraction)
Option C
D
(StartFraction 13 over 52 EndFraction) (StartFraction 13 over 51 EndFraction) (StartFraction 13 over 50 EndFraction)
Option D
23

Li designed a survey to determine how comfortable students at her middle school are with fractions. There are 600 students in her middle school. The students are equally distributed among grade levels. She selected a sample of 28 students in her first-period class. Which best explains Li’s sample?

A
random and biased
B
random and unbiased
C
nonrandom and biased
D
nonrandom and unbiased
24

Which characteristics describe the scatterplot? Check all that apply.

Question illustration
A
negative correlation
B
positive correlation
C
strong association
D
weak association
E
linear
F
nonlinear
25

The probability for event A is 0.3, the probability for event B is 0.6, and the probability of events A or B is 0.8.Why are the events not mutually exclusive?

A
The sum of P(A) and P(B) is less than P(A or B).
B
The product of P(A) and P(B) is less than P(A or B).
C
The product of P(A) and P(B) is not equal to P(A or B).
D
The sum of P(A) and P(B) is not equal to P(A or B).
26

The large rectangle was reduced to create the small rectangle. Not drawn to scaleWhat is the missing measure on the small rectangle?

Question illustration
A
2 inches
B
3 inches
C
4 inches
D
5 inches
27

Julio is selecting a random sample of people to survey for a newspaper article. Which elements are important for Julio to consider when choosing a random sample? Select three options.

A
the size of the population
B
the size of the sample
C
the characteristics and demographics of the population
D
the probable responses to the survey questions from the population
E
the probable responses to the survey questions from the sample
28

The radius and circumference of several objects were measured.

Question illustration
A
It is a weak positive correlation, and it is not likely causal.
B
It is a weak positive correlation, and it is likely causal.
C
It is a strong positive correlation, and it is not likely causal.
D
It is a strong positive correlation, and it is likely causal.
29

The diagram represents a triangle that is reduced by a scale factor of 0.4. What is the height of the original triangle?

Question illustration
A
0.8 inches
B
2.4 inches
C
5 inches
D
8 inches
30

Out of a population of 1,500 students, 100 were asked by a random sampling to choose their favorite national park. Their responses are shown in the table below.National ParksFavorite ParkNumber of StudentsAcadia19Carlsbad Caverns14Rocky Mountain30Grand Canyon23Yosemite14Using proportional reasoning, about how many students out of the 1,500 would you expect to pick Yosemite for their favorite national park?

A
14
B
86
C
210
D
244
31

The list below shows all of the possible outcomes for flipping four coins.HHHHHHHTHHTHHHTTHTHHHTHTHTTHHTTTTHHHTHHTTHTHTHTTTTHHTTHTTTTHTTTTWhat is the probability of getting the same number of heads and tails?

A
StartFraction 1 over 8 EndFraction
Option A
B
One-fourth
Option B
C
StartFraction 3 over 8 EndFraction
Option C
D
Three-fourths
Option D
32

A company sells name plates for doors. An employee takes a random sample of name plates, measures the length of each name (in inches), and counts the number of letters in each name. She generates the scatterplot and trend line equation shown below. Name PlatesA customer would like the company to build him a name plate that is 22 inches long. What is the best estimate of the number of letters the company can have on the name plate?

Question illustration
A
9
B
10
C
12
D
39
33

Nico measured the water level in his pool every other day for two weeks. Which statement best describes the information shown by the scatterplot and trend line.

Question illustration
A
As the number of days increased, the water level always decreased.
B
As the number of days increased, the water level always increased.
C
As the number of days increased, the water level usually decreased.
D
As the number of days increased, the water level usually increased.
34

The box plots show the distributions of weights of cucumbers and zucchini collected from a garden. Which statement explains the best measure of variability to use to compare the data sets?

Question illustration
A
The mean is the best measure because the data sets have the same minimum weight.
B
The range is the best measure because the distribution of zucchini weights is skewed left.
C
The median is the best measure because the data sets have different medians.
D
The standard deviation is the best measure because both data distributions are symmetric.
35

A graph shows the horizontal axis numbered 4 to 16 and the vertical axis numbered 4 to 12. Points and a line show an upward trend.

Question illustration
A
–0.872
B
–0.191
C
0.191
D
0.872
36

Genevieve is buying a car audio system that consists of a stereo, speakers, and amplifiers. She is choosing between 5 types of stereos and 2 types of amplifiers. If she has a total of 30 choices, how many types of speakers must there be?

A
3
B
6
C
10
D
20
37

The data set represents the number of rings each person in a room is wearing.0, 2, 4, 0, 2, 3, 2, 8, 6What is the interquartile range of the data?

A
2
B
3
C
4
D
6
38

Administrators surveyed students enrolled in a new school in order to choose the school mascot. There are 480 students enrolled in the school. What is the proportion needed to calculate the average number of students that chose the lion for the mascot?Mascot SurveySample 1Sample 2Ducks12Ducks8Grizzlies24Grizzlies30Lions20Lions22Silverbacks16Silverbacks12

A
StartFraction 21 over 72 EndFraction = StartFraction x over 480 EndFraction
Option A
B
StartFraction 72 over 21 EndFraction = StartFraction x over 480 EndFraction
Option B
C
StartFraction 42 over 72 EndFraction = StartFraction x over 480 EndFraction
Option C
D
StartFraction 20 over 22 EndFraction = StartFraction x over 480 EndFraction
Option D
39

Researchers compare the body composition of cattle feeding on a grain diet with that of cattle feeding on a grass diet. This method of gathering data is classified as

A
a census.
B
a sample survey.
C
an experiment.
D
an observational study.
40

Consider the enlargement of the triangle. Not drawn to scaleRounded to the nearest tenth, what is the value of x?

Question illustration
A
15.8 feet
B
19.1 feet
C
23.3 feet
D
32.6 feet

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