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A poll conducted by Pugh Research found 75% of Americans want the next president to be middle-aged (35-65 years old). 57% responded that they preferred a president willing to compromise on issues to accomplish action rather than make decisions strictly along partisan ideals. 48% of the respondents fell into both categories. d. How many Americans do we expect to select before finding the first one who belongs to both categories? Interpret this result. e. What is the likelihood exactly 14 Americans in a random group of 22 believe the next president should be middle- aged? f. What is the probability at most 8 Americans in a random group of 60 belong only to the category of wanting a president that is willing to compromise on issues?

A poll conducted by Pugh Research found 75% of Americans want the next president to be middle-aged (35-65 years old). 57% responded that they preferred a president willing to compromise on issues to accomplish action rather than make decisions strictly along partisan ideals. 48% of the respondents fell into both categories. d. How many Americans do we expect to select before finding the first one who belongs to both categories? Interpret this result. e. What is the likelihood exactly 14 Americans in a random group of 22 believe the next president should be middle- aged? f. What is the probability at most 8 Americans in a random group of 60 belong only to the category of wanting a president that is willing to compromise on issues?

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Bernoulli Trials - Question 2.1 Please solve with simple probability rules
### Poll Result Analysis: Preferences for the Next U.S. President #### Poll Findings by Pugh Research: A survey conducted by Pugh Research unveiled the opinions of Americans regarding the characteristics they desire in the next president. The primary findings are as follows: 1. **Age Preference**: 75% of Americans expressed a preference for a middle-aged president (between 35-65 years old). 2. **Decision-Making Approach**: 57% of respondents indicated that they prefer a president inclined to compromise on various issues to achieve actionable results rather than making decisions solely along partisan lines. 3. **Combined Preference**: Notably, 48% of the participants favored a president who fits both aforementioned characteristics. #### Questions for Further Analysis: **d. Expected Number of Selections:** - **Question**: How many Americans do we expect to select before finding the first one who belongs to both categories? - **Interpretation**: To solve this, we need to consider the probability of selecting an individual who fits both categories (48%). Using the geometric distribution, we can calculate the expected number of selections. **e. Likelihood of Middle-Aged Preference in a Sample:** - **Question**: What is the likelihood that exactly 14 Americans out of a randomly selected group of 22 believe the next president should be middle-aged? - **Interpretation**: This can be approached using the binomial distribution, where the probability \( p \) is 75% (0.75) for middle-aged preference. **f. Probability of Willingness to Compromise in a Sample:** - **Question**: What is the probability that at most 8 Americans in a random group of 60 belong only to the category of wanting a president willing to compromise on issues? - **Interpretation**: Here, we need to focus on the 57% who want a compromising president, but the trick is to exclude those who also want a middle-aged president (to avoid the overlap). We are dealing with the cumulative probability distribution to find the likelihood for at most 8 Americans in the group of 60. These questions aim to provide deeper insights into the demographic and attitudinal patterns observed in the poll, utilizing probability distributions for precise quantification.
Transcribed Image Text:### Poll Result Analysis: Preferences for the Next U.S. President #### Poll Findings by Pugh Research: A survey conducted by Pugh Research unveiled the opinions of Americans regarding the characteristics they desire in the next president. The primary findings are as follows: 1. **Age Preference**: 75% of Americans expressed a preference for a middle-aged president (between 35-65 years old). 2. **Decision-Making Approach**: 57% of respondents indicated that they prefer a president inclined to compromise on various issues to achieve actionable results rather than making decisions solely along partisan lines. 3. **Combined Preference**: Notably, 48% of the participants favored a president who fits both aforementioned characteristics. #### Questions for Further Analysis: **d. Expected Number of Selections:** - **Question**: How many Americans do we expect to select before finding the first one who belongs to both categories? - **Interpretation**: To solve this, we need to consider the probability of selecting an individual who fits both categories (48%). Using the geometric distribution, we can calculate the expected number of selections. **e. Likelihood of Middle-Aged Preference in a Sample:** - **Question**: What is the likelihood that exactly 14 Americans out of a randomly selected group of 22 believe the next president should be middle-aged? - **Interpretation**: This can be approached using the binomial distribution, where the probability \( p \) is 75% (0.75) for middle-aged preference. **f. Probability of Willingness to Compromise in a Sample:** - **Question**: What is the probability that at most 8 Americans in a random group of 60 belong only to the category of wanting a president willing to compromise on issues? - **Interpretation**: Here, we need to focus on the 57% who want a compromising president, but the trick is to exclude those who also want a middle-aged president (to avoid the overlap). We are dealing with the cumulative probability distribution to find the likelihood for at most 8 Americans in the group of 60. These questions aim to provide deeper insights into the demographic and attitudinal patterns observed in the poll, utilizing probability distributions for precise quantification.
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