Table of contents

1. Intro to Stats and Collecting Data55m
2. Describing Data with Tables and Graphs1h 55m
3. Describing Data Numerically1h 45m
4. Probability2h 16m
5. Binomial Distribution & Discrete Random Variables2h 33m
6. Normal Distribution and Continuous Random Variables1h 38m
7. Sampling Distributions & Confidence Intervals: Mean1h 53m
8. Sampling Distributions & Confidence Intervals: Proportion1h 12m
- Sampling Distribution of Sample Proportion
  29m
- Confidence Intervals for Population Proportion
  42m
9. Hypothesis Testing for One Sample2h 19m
10. Hypothesis Testing for Two Samples3h 22m
11. Correlation1h 6m
12. Regression1h 4m
13. Chi-Square Tests & Goodness of Fit1h 20m
14. ANOVA1h 0m

5. Binomial Distribution & Discrete Random Variables

Binomial Distribution

Statistics

5. Binomial Distribution & Discrete Random Variables

Binomial Distribution

Previous problemNext problem

1:28 minutes

Problem 4.1.21a

Textbook Question

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

Verified step by step guidance

Step 1: Recall the probability distribution created in Exercise 19. A probability distribution lists all possible outcomes (e.g., the number of HD televisions in a household) and their corresponding probabilities. Ensure that the probabilities sum to 1.

Step 2: Identify the outcomes of interest. In this case, we are looking for households with either one or two HD televisions. These correspond to the outcomes '1' and '2' in the probability distribution.

Step 3: Locate the probabilities associated with the outcomes '1' and '2' in the probability distribution. These probabilities are denoted as P(X=1) and P(X=2), where X represents the number of HD televisions.

Step 4: Add the probabilities of the outcomes '1' and '2' together to find the total probability. Use the formula: P(X=1 or X=2) = P(X=1) + P(X=2).

Step 5: Verify that the result is valid by ensuring it falls within the range of 0 to 1, as probabilities cannot exceed these bounds.

Verified video answer for a similar problem:

This video solution was recommended by our tutors as helpful for the problem above

Video duration:

Play a video:

Was this helpful?

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.

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 and conclusions. In the context of the question, it implies that each household has an equal opportunity to be chosen when assessing the number of HD televisions.

Event Probability

Event probability is the measure of the likelihood that a specific event will occur, expressed as a number between 0 and 1. In this case, it involves calculating the probability of selecting a household with one or two HD televisions based on the provided distribution. Understanding how to compute event probabilities is fundamental for making predictions and informed decisions based on statistical data.

Watch next

Master The Binomial Experiment with a bite sized video explanation from Patrick

Start learning

Related Videos

Related Practice

Textbook Question

Forty-nine percent of U.S. adults think that human activity such as burning fossil fuels contributes a great deal to climate change. You randomly select 25 U.S. adults. Find the probability that the number who think that human activity contributes a great deal to climate change is (a) exactly 12,

In Exercises 1–7, consider a grocery store that can process a total of four customers at its checkout counters each minute.

The mean number of customers who arrive at the checkout counters each minute is 4. Create a Poisson distribution with mu = 4 for x = 0 to 20. Compare your results with the histogram shown at the upper right.

views

Textbook Question

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

views

Textbook Question

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,

views

Textbook Question

Finding Probabilities Use the probability distribution you made in Exercise 19 to find the probability of randomly selecting a household that has (d) at most two HD televisions.

views

Textbook Question

In Exercises 1–7, consider a grocery store that can process a total of four customers at its checkout counters each minute.

The mean number of arrivals per minute is four. Find the probability that

a. three, four, or five customers will arrive during the third minute.

views

Show more practices

Download the Mobile app

Privacy

Do not sell my personal information

Accessibility

Patent notice

Sitemap