Assume That 12 Jurors Are Randomly Selected From A Population In Which 71% Of The People Are Mexican-Americans. Refer To The Probability Distribution Table Below And Find The Indicated Probabilities.$\[ \begin{tabular}{|r|r|} \hline $x$ & $P(x)$
Probability Distribution of Mexican-Americans in a Jury
In this article, we will explore the concept of probability distribution and its application in a real-world scenario. We will assume that 12 jurors are randomly selected from a population in which 71% of the people are Mexican-Americans. Our goal is to find the indicated probabilities using the given probability distribution table.
Probability distribution is a mathematical concept that describes the probability of each possible outcome in a random experiment. It is a function that assigns a probability to each possible outcome, and it is used to model the behavior of random variables. In this case, we are interested in finding the probability of selecting a certain number of Mexican-Americans in a jury of 12.
The Probability Distribution Table
The probability distribution table below shows the probability of selecting a certain number of Mexican-Americans in a jury of 12.
| 0 | 0.0003 |
| 1 | 0.0036 |
| 2 | 0.0273 |
| 3 | 0.1044 |
| 4 | 0.2245 |
| 5 | 0.2763 |
| 6 | 0.2245 |
| 7 | 0.1044 |
| 8 | 0.0273 |
| 9 | 0.0036 |
| 10 | 0.0003 |
| 11 | 0.0000 |
| 12 | 0.0000 |
Finding the Indicated Probabilities
We are interested in finding the probability of selecting 4, 6, and 8 Mexican-Americans in a jury of 12.
Probability of Selecting 4 Mexican-Americans
To find the probability of selecting 4 Mexican-Americans, we need to look at the probability distribution table and find the value of . According to the table, .
Probability of Selecting 6 Mexican-Americans
To find the probability of selecting 6 Mexican-Americans, we need to look at the probability distribution table and find the value of . According to the table, .
Probability of Selecting 8 Mexican-Americans
To find the probability of selecting 8 Mexican-Americans, we need to look at the probability distribution table and find the value of . According to the table, .
In this article, we have explored the concept of probability distribution and its application in a real-world scenario. We have assumed that 12 jurors are randomly selected from a population in which 71% of the people are Mexican-Americans. Using the given probability distribution table, we have found the indicated probabilities of selecting 4, 6, and 8 Mexican-Americans in a jury of 12.
- [1] Probability Distribution. (n.d.). In Wikipedia. Retrieved from https://en.wikipedia.org/wiki/Probability_distribution
- [2] Mexican-American Population. (n.d.). In United States Census Bureau. Retrieved from https://www.census.gov/topics/population/hispanic.html
| 0 | 0.0003 | |
| 1 | 0.0036 | |
| 2 | 0.0273 | |
| 3 | 0.1044 | |
| 4 | 0.2245 | |
| 5 | 0.2763 | |
| 6 | 0.2245 | |
| 7 | 0.1044 | |
| 8 | 0.0273 | |
| 9 | 0.0036 | |
| 10 | 0.0003 | |
| 11 | 0.0000 | |
| 12 | 0.0000 |
Frequently Asked Questions (FAQs) about Probability Distribution
In our previous article, we explored the concept of probability distribution and its application in a real-world scenario. We assumed that 12 jurors are randomly selected from a population in which 71% of the people are Mexican-Americans. Using the given probability distribution table, we found the indicated probabilities of selecting 4, 6, and 8 Mexican-Americans in a jury of 12. In this article, we will answer some frequently asked questions (FAQs) about probability distribution.
Q: What is probability distribution?
A: Probability distribution is a mathematical concept that describes the probability of each possible outcome in a random experiment. It is a function that assigns a probability to each possible outcome, and it is used to model the behavior of random variables.
Q: What is the difference between probability distribution and probability?
A: Probability distribution is a function that assigns a probability to each possible outcome, while probability is a measure of the likelihood of an event occurring. Probability distribution is used to model the behavior of random variables, while probability is used to describe the likelihood of a specific event.
Q: How is probability distribution used in real-world scenarios?
A: Probability distribution is used in a wide range of real-world scenarios, including finance, engineering, and social sciences. For example, it is used to model the behavior of stock prices, to predict the outcome of elections, and to understand the behavior of complex systems.
Q: What are the types of probability distribution?
A: There are several types of probability distribution, including:
- Discrete probability distribution: This type of distribution is used to model the behavior of random variables that can take on a finite number of values.
- Continuous probability distribution: This type of distribution is used to model the behavior of random variables that can take on any value within a given range.
- Mixed probability distribution: This type of distribution is used to model the behavior of random variables that can take on both discrete and continuous values.
Q: How is probability distribution used in statistics?
A: Probability distribution is used in statistics to model the behavior of random variables and to make inferences about a population based on a sample of data. It is used to calculate probabilities, to estimate parameters, and to test hypotheses.
Q: What is the importance of probability distribution in decision-making?
A: Probability distribution is important in decision-making because it allows us to model the behavior of random variables and to make informed decisions based on probabilities. It is used in a wide range of decision-making scenarios, including finance, engineering, and social sciences.
Q: How can I learn more about probability distribution?
A: There are many resources available to learn more about probability distribution, including textbooks, online courses, and research papers. Some popular resources include:
- Khan Academy: Khan Academy offers a comprehensive course on probability and statistics.
- Coursera: Coursera offers a wide range of courses on probability and statistics.
- Research papers: Research papers on probability distribution can be found on academic databases such as Google Scholar and JSTOR.
In this article, we have answered some frequently asked questions (FAQs) about probability distribution. We have discussed the concept of probability distribution, its types, and its applications in real-world scenarios. We have also provided some resources for learning more about probability distribution.