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Ch. 4 - Discrete Probability Distributions
Larson - Elementary Statistics: Picturing the World 8th Edition
Larson8th EditionElementary Statistics: Picturing the WorldISBN: 9780137493470Not the one you use?Change textbook
All textbooksLarson 8th EditionCh. 4 - Discrete Probability DistributionsProblem 4.R.1
Chapter 4, Problem 4.R.1

In Exercises 1 and 2, determine whether the random variable x is discrete or continuous. Explain.


Let x represent the grade on an exam worth a total of 100 points.

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1
Understand the definitions: A discrete random variable takes on a countable number of distinct values, while a continuous random variable can take on any value within a given range, including fractions and decimals.
Identify the nature of the variable x: The grade on an exam worth a total of 100 points is typically expressed as a whole number (e.g., 85, 90, etc.), which suggests it is countable.
Consider whether fractional values are possible: If grades are rounded to whole numbers, x is discrete. However, if fractional grades (e.g., 85.5) are allowed, x could be continuous.
Determine the context: In most grading systems, grades are reported as whole numbers, making x a discrete random variable.
Explain the conclusion: Since the grade is typically a countable value and does not take on an infinite range of possibilities within an interval, x is classified as a discrete random variable.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Discrete Random Variable

A discrete random variable is one that can take on a countable number of distinct values. Examples include the number of students in a class or the outcome of rolling a die. In the context of grades, if we consider only whole number scores (0, 1, 2, ..., 100), the variable is discrete because it cannot take on values like 75.5.
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Continuous Random Variable

A continuous random variable can take on an infinite number of values within a given range. This means it can represent measurements that can be infinitely divided, such as height or weight. If grades were measured with decimals (e.g., 75.5), then the variable would be considered continuous, as it could take any value within the range of possible scores.
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Random Variable

A random variable is a numerical outcome of a random phenomenon. It can be classified as either discrete or continuous based on the nature of its possible values. Understanding whether a random variable is discrete or continuous is crucial for selecting appropriate statistical methods for analysis, such as probability distributions.
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Related Practice
Textbook Question

In Exercises 21–26, find the indicated probabilities using the geometric distribution, the Poisson distribution, or the binomial distribution. Then determine whether the events are unusual. If convenient, use a table or technology to find the probabilities

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Textbook Question

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a. Construct a binomial distribution.

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Textbook Question

In Exercises 21–26, find the indicated probabilities using the geometric distribution, the Poisson distribution, or the binomial distribution. Then determine whether the events are unusual. If convenient, use a table or technology to find the probabilities.

Fourteen percent of noninstitutionalized U.S. adults smoke cigarettes. After randomly selecting ten noninstitutionalized U.S. adults, you ask them whether they smoke cigarettes. Find the probability that the first adult who smokes cigarettes is (c) not one of the first six persons selected.

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Textbook Question

In Exercises 21–26, find the indicated probabilities using the geometric distribution, the Poisson distribution, or the binomial distribution. Then determine whether the events are unusual. If convenient, use a table or technology to find the probabilities

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Textbook Question

The table lists the number of wireless devices per household in a small town in the United States.

c. Find the mean, variance, and standard deviation of the probability distribution and interpret the results.

Textbook Question

The table lists the number of wireless devices per household in a small town in the United States.

a. Construct a probability distribution.