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Ch. 4 - Discrete Probability Distributions
Larson - Elementary Statistics: Picturing the World 8th Edition
Larson8th EditionElementary Statistics: Picturing the WorldISBN: 9780137493470당신이 사용하는 게 아니라요?교과서 변경
4장, 문제 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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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

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.
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Calculating Probabilities in a Binomial Distribution

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.
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가이드 코스
07:09
Intro to Random Variables & Probability Distributions

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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Introduction to Probability
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교과서 질문

Using a Distribution to Find Probabilities In Exercises 11–26, 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.


Oil Tankers In the month of June 2021, 240 oil tankers stop at a port city. No oil tanker visits more than once. Find the probability that the number of oil tankers that stop on any given day in June is (c) more than eight.

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교과서 질문

Using a Distribution to Find Probabilities In Exercises 11–26, 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.


Living Donor Transplants The mean number of organ transplants from living donors performed per day in the United States in 2020 was about 16. Find the probability that the number of organ transplants from living donors performed on any given day is (c) no more than 10. (Source: Organ Procurement and Transplantation Network)

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교과서 질문

Manufacturing An assembly line produces 10,000 automobile parts. Twenty percent of the parts are defective. An inspector randomly selects 10 of the parts


b. Because the sample is only 0.1% of the population, treat the events as independent and use the binomial probability formula to approximate the probability that none of the selected parts are defective.

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교과서 질문

Unusual Events In Exercises 37 and 38, find the indicated probabilities. Then determine if the event is unusual. Explain your reasoning.


Rock-Paper-Scissors The probability of winning a game of rock-paper-scissors is 1/3. You play nine games of rock-paper-scissors. Find the probability that the number of games you win is (c) less than two.

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교과서 질문

Using a Distribution to Find Probabilities In Exercises 11–26, 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.


Living Donor Transplants The mean number of organ transplants from living donors performed per day in the United States in 2020 was about 16. Find the probability that the number of organ transplants from living donors performed on any given day is (b) at least eight (Source: Organ Procurement and Transplantation Network)

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교과서 질문

Hypergeometric Distribution Binomial experiments require that any sampling be done with replacement because each trial must be independent of the others. The hypergeometric distribution also has two outcomes: success and failure. The sampling, however, is done without replacement. For a population of N items having k successes and failures, the probability of selecting a sample of size that has successes and failures is given by

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In a shipment of 15 microchips, 2 are defective and 13 are not defective. A sample of three microchips is chosen at random. Use the above formula to find the probability that (c) two microchips are defective and one is not defective.

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