AP®StatisticsCollege BoardExam QuestionsUnit 4: Probability, Random Variables & Probability DistributionsDiscrete Random Variables

Discrete Random Variables (College Board AP® Statistics)

Exam Questions

6 mins6 questions
1
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A company sells chairs in batches of four. The probability distribution of X, the number of chairs sold in a single order from this company, is shown in the table below.

x

4

8

12

16

P open parentheses X equals x close parentheses

0.5

0.2

0.2

0.1

The expected value of the probability distribution of X is 7.6, and the standard deviation is 4.18. The profit Y, in dollars, for a particular order is given by Y equals 20 X minus 30. What is the standard deviation of Y?

  • $53.60

  • $83.60

  • $113.60

  • $152.00

  • $1,672.00

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2
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At the end of a level in a video game, a player can score 0, 10, 50, or 100 points. Let the random variable X represent the number of points scored by a player at the end of a level. The expected value of X is 15.5 points. What is the meaning of the expected value in this context?

  • Every player will score 15.5 points at the end of the level.

  • Players score an average of 15.5 points at the end of the level.

  • Players are guaranteed to score at least 10 points at the end of the level.

  • 15.5 percent of all players will score 100 points.

  • A score of 100 points is the most likely outcome.

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3
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Sun and Jin sit next to each other on a flight. There is a 60 percent chance that Sun will fall asleep during the flight. If Sun falls asleep, there is a 70 percent chance that Jin will also fall asleep. If Sun does not fall asleep, there is a 20 percent chance that Jin will fall asleep. Let X be the number of them that fall asleep during the flight.

Which of the following tables shows the probability distribution of X?

  • x

    0

    1

    2

    p open parentheses x close parentheses

    1 third

    1 third

    1 third

  • x

    0

    1

    2

    p open parentheses x close parentheses

    1 fourth

    1 half

    1 fourth

  • x

    0

    1

    2

    p open parentheses x close parentheses

    0.32

    0.26

    0.42

  • x

    0

    1

    2

    p open parentheses x close parentheses

    0.32

    0.08

    0.42

  • x

    0

    1

    2

    p open parentheses x close parentheses

    0.60

    0.20

    0.70

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4
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A college entrance exam contains multiple-choice questions and is designed to prevent students from choosing answers at random. For each correct answer, a student scores ten points. For each question left unanswered, a student scored three points. For each incorrect answer, a student scores zero points. Each question has seven choices. What is the minimum number of answer choices a student should rule out before guessing becomes a strategic advantage?

  • 0

  • 1

  • 2

  • 3

  • 4

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5
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A bag contains a large number of tokens. Each token has a number written on it. Let X represent the number written on a token when that token is selected at random from the bag. The expected value of X is 8.5, and the standard deviation is approximately 3.14.

Mark selects a token at random, records the number, and returns the token to the bag. Mark then selects another token at random and subtracts the number written on the second token from the number written on the first token. Which of the following values is closest to the standard deviation of Mark's answer?

  • 0

  • 3.14

  • 4.44

  • 6.28

  • 19.72

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6
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Dinah's Diner is famous for selling triple burgers. The triple burger consists of three beef patties, two slices of bacon, and one toasted bread bun. The distributions of weights for the items are each approximately normal. The mean and standard deviation for each distribution are shown in the table below. The weights of the items are assumed to be independent.

Item

Mean

Standard deviation

Beef patty

4.3 ounces

0.61 ounces

Slice of bacon

2.4 ounces

0.43 ounces

Toasted bread bun

1.8 ounces

0.72 ounces

Let the random variable W represent the total weight of the triple burger. Which of the following is closest to the standard deviation of W?

  • 1.42 ounces

  • 1.76 ounces

  • 2.15 ounces

  • 2.82 ounces

  • 3.41 ounces

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