Assume That 12 Jurors Are Randomly Selected From A Population In Which $77\%$ Of The People Are Mexican-Americans. Refer To The Probability Distribution Table Below And Find The Indicated

Introduction

In this article, we will be discussing the concept of probability distribution and how it applies to a real-world scenario. We are given a population in which $77%$ of the people are Mexican-Americans, and we are asked to find the probability of selecting a certain number of Mexican-Americans from a group of 12 randomly selected jurors.

The Probability Distribution Table

Understanding the Table

The table above shows the probability of selecting a certain number of Mexican-Americans from a group of 12 randomly selected jurors. The probabilities are calculated using the binomial distribution formula, which takes into account the probability of success (in this case, selecting a Mexican-American) and the number of trials (in this case, the number of jurors selected).

Calculating the Probability

To calculate the probability of selecting a certain number of Mexican-Americans, we need to use the binomial distribution formula. The formula is given by:

$$P(X=k) = \binom{n}{k} p^k (1-p)^{n-k}$$

where:

• $P(X=k)$ is the probability of selecting $k$ Mexican-Americans
• $\binom{n}{k}$ is the number of combinations of $n$ items taken $k$ at a time
• $p$ is the probability of selecting a Mexican-American (in this case, 0.77)
• $n$ is the number of jurors selected (in this case, 12)
• $k$ is the number of Mexican-Americans selected

Finding the Indicated Probability

We are asked to find the probability of selecting 4 Mexican-Americans from a group of 12 randomly selected jurors. Using the binomial distribution formula, we can calculate the probability as follows:

$$P(X=4) = \binom{12}{4} (0.77)^4 (1-0.77)^{12-4}$$

$$P(X=4) = 495 (0.77)^4 (0.23)^8$$

$$P(X=4) = 0.3085$$

Conclusion

In this article, we discussed the concept of probability distribution and how it applies to a real-world scenario. We were given a population in which $77%$ of the people are Mexican-Americans, and we were asked to find the probability of selecting a certain number of Mexican-Americans from a group of 12 randomly selected jurors. Using the binomial distribution formula, we calculated the probability of selecting 4 Mexican-Americans and found it to be 0.3085.

The Importance of Probability Distribution

Probability distribution is an important concept in mathematics and statistics. It is used to model real-world scenarios and make predictions about the outcome of events. In this article, we saw how probability distribution can be used to calculate the probability of selecting a certain number of Mexican-Americans from a group of 12 randomly selected jurors.

Real-World Applications of Probability Distribution

Probability distribution has many real-world applications. It is used in fields such as finance, engineering, and medicine to make predictions about the outcome of events. For example, in finance, probability distribution is used to calculate the risk of investments and make predictions about the future value of stocks. In engineering, probability distribution is used to design and optimize systems, such as bridges and buildings. In medicine, probability distribution is used to make predictions about the outcome of medical treatments and diagnose diseases.

Conclusion

In conclusion, probability distribution is an important concept in mathematics and statistics. It is used to model real-world scenarios and make predictions about the outcome of events. In this article, we discussed the concept of probability distribution and how it applies to a real-world scenario. We calculated the probability of selecting 4 Mexican-Americans from a group of 12 randomly selected jurors and found it to be 0.3085. We also discussed the importance of probability distribution and its real-world applications.

References

• [1] "Probability Distribution" by Wikipedia
• [2] "Binomial Distribution" by MathWorld
• [3] "Probability Distribution in Finance" by Investopedia
• [4] "Probability Distribution in Engineering" by Engineering.com
• [5] "Probability Distribution in Medicine" by Medscape