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 4.1.21b

Chapter 4, Problem 4.1.21b

Finding Probabilities Use the probability distribution you made in Exercise 19 to find the probability of randomly selecting a household that has (b) two or more HD televisions

Verified step by step guidance

Step 1: Recall the probability distribution created in Exercise 19. This distribution should list the number of HD televisions in a household (e.g., 0, 1, 2, etc.) along with their corresponding probabilities.

Step 2: Identify the probabilities associated with households that have two or more HD televisions. This means you need to consider the probabilities for 2, 3, and any higher numbers of HD televisions (if applicable).

Step 3: Add the probabilities for all these cases (e.g., P(X = 2), P(X = 3), etc.). Use the formula: \( P(X \geq 2) = P(X = 2) + P(X = 3) + \dots \).

Step 4: Ensure that the sum of all probabilities in the distribution equals 1. This is a good way to verify that the distribution is valid and that no probabilities are missing.

Step 5: The result of the summation from Step 3 gives the probability of randomly selecting a household with two or more HD televisions.

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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 selecting households with certain characteristics.

Random Selection

Random selection refers to the process of choosing individuals or items from a larger 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 to be made. In the context of the question, it implies that the households are chosen without bias, which is important for accurate probability calculations.

Cumulative Probability

Cumulative probability is the probability that a random variable takes on a value less than or equal to a specific value. In the context of the question, finding the probability of selecting a household with two or more HD televisions involves calculating the cumulative probability for that category. This concept helps in understanding how probabilities accumulate across different outcomes, which is essential for answering questions about ranges or groups of outcomes.

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