Ch. 4 - Discrete Probability Distributions

Larson - Elementary Statistics: Picturing the World 8th Edition

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Larson 8th Edition

Ch. 4 - Discrete Probability Distributions

Problem 4.1.21c

Chapter 4, Problem 4.1.21c

Finding Probabilities Use the probability distribution you made in Exercise 19 to find the probability of randomly selecting a household that has (c) from one to three HD televisions,

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Identify the probability distribution created in Exercise 19. Ensure it lists all possible outcomes (number of HD televisions in a household) and their corresponding probabilities. Verify that the probabilities sum to 1, as required for a valid probability distribution.

Define the range of interest for this problem: households with 'from one to three HD televisions.' This means you are interested in the probabilities for households with 1, 2, and 3 HD televisions.

Extract the probabilities corresponding to the outcomes of 1, 2, and 3 HD televisions from the probability distribution table.

Add the probabilities for these outcomes together. Use the formula: \( P(1 \, \text{to} \, 3) = P(1) + P(2) + P(3) \).

Verify your result by ensuring the sum of the probabilities for all outcomes in the distribution still equals 1, confirming no errors in the calculation.

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Key Concepts

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

Probability Distribution

A probability distribution is a mathematical function that provides the probabilities of occurrence of different possible outcomes in an experiment. It can be discrete, where outcomes are distinct and countable, or continuous, where outcomes can take any value within a range. Understanding how to construct and interpret a probability distribution is essential for calculating probabilities related to specific events, such as the number of HD televisions in households.

Random Selection

Random selection refers to the process of choosing individuals or items from a population in such a way that each member has an equal chance of being selected. This concept is crucial in statistics as it helps ensure that the sample is representative of the population, allowing for valid inferences. In the context of the question, it implies that the households are chosen without bias, which is important for accurately determining the probability of having one to three HD televisions.

Cumulative Probability

Cumulative probability is the probability that a random variable takes on a value less than or equal to a specific value. In this case, to find the probability of selecting a household with one to three HD televisions, one would sum the probabilities of having one, two, and three televisions. This concept is vital for understanding how to aggregate probabilities from a distribution to answer specific questions about ranges of outcomes.

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Textbook Question

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Textbook Question

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Textbook Question

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Textbook Question

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Textbook Question

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