Problem-Solving and Data Analysis

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Problem-Solving and Data Analysis

CE

Chief Editor

Mar 27, 2024

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Take all 14 MCQs in interactive quiz mode with timer and progress tracking

Texting behavior Talks on cell phone daily Does not talk on cell phone daily Total Light 110146256 Medium 139164303 Heavy 16674240 Total 415384799 In a study of cell phone use, 799 randomly selected US teens were asked how often they talked on a cell phone and about their texting behavior. The data are summarized in the table above. Based on the data from the study, an estimate of the percentage of US teens who are heavy texters is 30% and the associated margin of error is 3%. Which of the following is a correct statement based on the given margin of error?

Difficulty: Hard

A:

Approximately 3% of the teens in the study who are classified as heavy texters are not really heavy texters.

B:

Each face of a fair 14-sided die is labeled with a number from 1 through 14, with a different number appearing on each face. If the die is rolled one time, what is the probability of rolling a 2?

C:

The percent of all US teens who are heavy texters is 33%.

D:

The International Space Station orbits Earth at an average speed of 4.76 miles per second. What is the space station's average speed in miles per hour?

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Each of the following frequency tables represents a data set. Which data set has the greatest mean?

Difficulty: Hard

A:

Texting behavior Talks on cell phone daily Does not talk on cell phone daily Total Light 110146256 Medium 139164303 Heavy 16674240 Total 415384799 In a study of cell phone use, 799 randomly selected US teens were asked how often they talked on a cell phone and about their texting behavior. The data are summarized in the table above. Based on the data from the study, an estimate of the percentage of US teens who are heavy texters is 30% and the associated margin of error is 3%. Which of the following is a correct statement based on the given margin of error?

B:

Value Frequency 7068069061006

C:

Value Frequency 7078069061007

D:

Value Frequency 7088059051008

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Each face of a fair 14-sided die is labeled with a number from 1 through 14, with a different number appearing on each face. If the die is rolled one time, what is the probability of rolling a 2?

Difficulty: Easy

A:

\frac{1}{14}

B:

\frac{2}{14}

C:

\frac{12}{14}

D:

\frac{13}{14}

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There are 55 students in Spanish club. A sample of the Spanish club students was selected at random and asked whether they intend to enroll in a new study program. Of those surveyed, 20% responded that they intend to enroll in the study program. Based on this survey, which of the following is the best estimate of the total number of Spanish club students who intend to enroll in the study program?

Difficulty: Easy

A:

11

B:

20

C:

44

D:

55

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Jennifer bought a box of Crunchy Grain cereal. The nutrition facts on the box state that a serving size of the cereal is $\frac{3}{4}$ cup and provides 210 calories, 50 of which are calories from fat. In addition, each serving of the cereal provides 180 milligrams of potassium, which is 5% of the daily allowance for adults. If $p$ percent of an adult’s daily allowance of potassium is provided by $x$ servings of Crunchy Grain cereal per day, which of the following expresses $p$ in terms of $x$?

Difficulty: Hard

A:

$p=0.5x$

B:

$p =5x$

C:

p=(0.05)^{x}

D:

p=(1.05)^{5}

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Prices of 14 Different Cars Type of car Priced at no more than $25,000 Priced greater than $25,000 Total Nonhybrid 538 Hybrid 246 Total 7714 The table above shows information about 14 cars listed for sale on an auto dealership's website. If one of the cars listed for sale is selected at random, what is the probability that the car selected will be a hybrid car priced at no more than $25,000?

Difficulty: Medium

A:

\frac{1}{7}

B:

\frac{2}{7}

C:

\frac{1}{3}

D:

\frac{4}{7}

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Species of Tree Growth Factor Red Maple 4.5 River Birch 3.5 Cottonwood 2.0 Black Walnut 4.5 White Birch 5.0 American Elm 4.0 Pin Oak 3.0 Shagbark Hickory 7.5 One method of calculating the approximate age, in years, of a tree of a particular species is to multiply the diameter of the tree, in inches, by a constant called the growth factor for that species. The table above gives the growth factors for eight species of trees. If a white birch tree and a pin oak tree each now have a diameter of 1 foot, which of the following will be closest to the difference, in inches, of their diameters 10 years from now? (1 foot = 12 inches).

Difficulty: Hard

A:

1.0

B:

1.2

C:

1.3

D:

\frac{1}{7}

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The International Space Station orbits Earth at an average speed of 4.76 miles per second. What is the space station's average speed in miles per hour?

Difficulty: Medium

A:

285.6

B:

571.2

C:

856.8

D:

17,136.0

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The population density of Iceland, in people per square kilometer of land area, increased from 2.5 in 1990 to 3.3 in 2014. During this time period, the land area of Iceland was 100,250 square kilometers. By how many people did Iceland's population increase from 1990 to 2014?

Difficulty: Medium

A:

1.0

B:

1.2

C:

1.3

D:

1.4

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The International Space Station orbits Earth at an average speed of 4.76 miles per second. What is the space station's average speed in miles per hour?

Difficulty: Easy

A:

2

B:

3

C:

4

D:

9

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A sample of 40 fourth-grade students was selected at random from a certain school. The 40 students completed a survey about the morning announcements, and 32 thought the announcements were helpful. Which of the following is the largest population to which the results of the survey can be applied?

Difficulty: Hard

A:

The 40 students who were surveyed

B:

All fourth-grade students at the school

C:

All students at the school

D:

All fourth-grade students in the county in which the school is located

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Residents of a town were surveyed to determine whether they were satisfied with the concession stand at the local park. A random sample of 200 residents was selected. All 200 responded, and 87% said they were satisfied. Based on this information, which of the following statements must be true? $I$. Of all the town residents, 87% would say they are satisfied with the concession stand at the local park. $II$. If another random sample of 200 residents were surveyed, 87% would say they are satisfied.

Difficulty: Medium

A:

Neither

B:

$I$ only

C:

$II$ only

D:

$I$ and $II$

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Ages of 20 Students Enrolled in a College Class Age Frequency 186195204212221231301 The table above shows the distribution of ages of the 20 students enrolled in a college class. Which of the following gives the correct order of the mean, median, and mode of the ages?

Difficulty: Medium

A:

mode $<$ median $<$ mean

B:

mode $<$ mean $<$ median

C:

median $<$ mode $<$ mean

D:

mean $<$ mode $<$ median

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Colors of Marbles in a Bag Color Number Red 8 Blue 10 Green 22 Total 40 The table shows the number of different colors of marbles in a bag. If a marble is chosen at random from the bag, what is the probability that the marble will be blue?

Difficulty: Easy

A:

\frac{30}{40}

B:

\frac{22}{40}

C:

\frac{18}{40}

D:

\frac{10}{40}

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