A. What is the number of trials? Answer: B. What is the probability of "success"? Answer: Chiny Ancor Do not round. C. What is the probability that no voters among the 13 selected would support this candidate?
A. What is the number of trials? Answer: B. What is the probability of "success"? Answer: Chiny Ancor Do not round. C. What is the probability that no voters among the 13 selected would support this candidate?
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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![### Binomial Probability Distribution Example
A recent survey in a particular state showed that only 24% of registered voters would support a certain candidate for U.S. Senate. Suppose that 13 registered voters from this state are selected at random. Assume that the binomial distribution applies.
**A. What is the number of trials?**
**Answer:** [ ]
---
**B. What is the probability of "success"?**
**Answer:** [ ]
*Do not round.*
---
**C. What is the probability that no voters among the 13 selected would support this candidate?**
**Answer:** [ ]
*Round to 4 decimal places.*
---
**D. What is the probability that exactly one voter from the sample selected would support this candidate?**
**Answer:** [ ]
*Round to 4 decimal places.*
---
**E. What is the probability that exactly 6 voters from the sample selected would support this candidate?**
**Answer:** [ ]
*Round to 4 decimal places.*
---
### Explanation
In this example, we are using the binomial probability distribution to model the likelihood of a certain number of successes in a series of independent trials. Here, a "success" is defined as a registered voter supporting the candidate.
- **Number of trials** (\( n \)) is the total number of registered voters selected, which is 13.
- **Probability of success** (\( p \)) is the percentage of voters who support the candidate, which is 24% or 0.24 in decimal form.
To calculate the probability for different scenarios (e.g., no voters supporting, exactly one voter supporting, exactly six voters supporting), we use the binomial probability formula:
\[ P(X = k) = \binom{n}{k} p^k (1-p)^{n-k} \]
Where:
- \( \binom{n}{k} \) is the binomial coefficient,
- \( k \) is the number of successes,
- \( p \) is the probability of success,
- \( (1-p) \) is the probability of failure,
- \( n \) is the number of trials.
Please ensure to use appropriate statistical tools or software to obtain the precise probabilities, and remember to round off your answers as instructed (to 4 decimal places where specified).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Faed2933e-b67f-42a0-9fac-b6dce0e828b0%2F0c77db65-0f9d-45ca-ba00-a670b6c1297a%2Fdlmkmui_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Binomial Probability Distribution Example
A recent survey in a particular state showed that only 24% of registered voters would support a certain candidate for U.S. Senate. Suppose that 13 registered voters from this state are selected at random. Assume that the binomial distribution applies.
**A. What is the number of trials?**
**Answer:** [ ]
---
**B. What is the probability of "success"?**
**Answer:** [ ]
*Do not round.*
---
**C. What is the probability that no voters among the 13 selected would support this candidate?**
**Answer:** [ ]
*Round to 4 decimal places.*
---
**D. What is the probability that exactly one voter from the sample selected would support this candidate?**
**Answer:** [ ]
*Round to 4 decimal places.*
---
**E. What is the probability that exactly 6 voters from the sample selected would support this candidate?**
**Answer:** [ ]
*Round to 4 decimal places.*
---
### Explanation
In this example, we are using the binomial probability distribution to model the likelihood of a certain number of successes in a series of independent trials. Here, a "success" is defined as a registered voter supporting the candidate.
- **Number of trials** (\( n \)) is the total number of registered voters selected, which is 13.
- **Probability of success** (\( p \)) is the percentage of voters who support the candidate, which is 24% or 0.24 in decimal form.
To calculate the probability for different scenarios (e.g., no voters supporting, exactly one voter supporting, exactly six voters supporting), we use the binomial probability formula:
\[ P(X = k) = \binom{n}{k} p^k (1-p)^{n-k} \]
Where:
- \( \binom{n}{k} \) is the binomial coefficient,
- \( k \) is the number of successes,
- \( p \) is the probability of success,
- \( (1-p) \) is the probability of failure,
- \( n \) is the number of trials.
Please ensure to use appropriate statistical tools or software to obtain the precise probabilities, and remember to round off your answers as instructed (to 4 decimal places where specified).
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