Seventy-one percent of adults want to live to age 100. You randomly select five adults and ask them whether they want to live to age 100. The random variable represents the number of adults who want to live to age 100. Complete parts (a) through (c) below. (a) Construct a binomial distribution. P(x) X 0 Q Search 1 2 3 4 5 (Round to five decimal places as needed.). View an example Get more help - Clear all om/Player/Player.aspx?cultureld=&theme=math&style=highered&disableStandbyIndicator=true&assignmentHandlesLocale=true 10/2
Seventy-one percent of adults want to live to age 100. You randomly select five adults and ask them whether they want to live to age 100. The random variable represents the number of adults who want to live to age 100. Complete parts (a) through (c) below. (a) Construct a binomial distribution. P(x) X 0 Q Search 1 2 3 4 5 (Round to five decimal places as needed.). View an example Get more help - Clear all om/Player/Player.aspx?cultureld=&theme=math&style=highered&disableStandbyIndicator=true&assignmentHandlesLocale=true 10/2
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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![**Educational Transcription:**
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**Probability and Statistics Problem: Constructing a Binomial Distribution**
**Problem Statement:**
Seventy-one percent of adults want to live to age 100. You randomly select five adults and ask them whether they want to live to age 100. The random variable represents the number of adults who want to live to age 100. Complete parts (a) through (c) below.
**Task (a): Construct a binomial distribution.**
- **Binomial Distribution Table:**
| x | P(x) |
|---|--------|
| 0 | |
| 1 | |
| 2 | |
| 3 | |
| 4 | |
| 5 | |
*(Round to five decimal places as needed.)*
---
**Explanation:**
This problem involves determining the probability of a specific number of adults, out of five, wanting to live to age 100, given that the probability of an individual adult wanting to reach that age is 71% (0.71). To solve this, you will need to use the binomial probability formula:
\[ P(x) = \binom{n}{x} p^x (1-p)^{n-x} \]
Where:
- \( n = 5 \) (the number of trials, i.e., adults surveyed),
- \( x \) (the number of successful outcomes, ranging from 0 to 5),
- \( p = 0.71 \) (the probability of success on each trial),
- \( \binom{n}{x} \) is the binomial coefficient.
Calculate \( P(x) \) for each value of \( x \) from 0 to 5 and fill in the table, rounding each probability to five decimal places.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F75f1adf9-8cfc-4785-9690-b40c37d251bd%2F3dea3834-a0f9-4e41-9140-5e6eb4e82303%2Fjja1b9e_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Educational Transcription:**
---
**Probability and Statistics Problem: Constructing a Binomial Distribution**
**Problem Statement:**
Seventy-one percent of adults want to live to age 100. You randomly select five adults and ask them whether they want to live to age 100. The random variable represents the number of adults who want to live to age 100. Complete parts (a) through (c) below.
**Task (a): Construct a binomial distribution.**
- **Binomial Distribution Table:**
| x | P(x) |
|---|--------|
| 0 | |
| 1 | |
| 2 | |
| 3 | |
| 4 | |
| 5 | |
*(Round to five decimal places as needed.)*
---
**Explanation:**
This problem involves determining the probability of a specific number of adults, out of five, wanting to live to age 100, given that the probability of an individual adult wanting to reach that age is 71% (0.71). To solve this, you will need to use the binomial probability formula:
\[ P(x) = \binom{n}{x} p^x (1-p)^{n-x} \]
Where:
- \( n = 5 \) (the number of trials, i.e., adults surveyed),
- \( x \) (the number of successful outcomes, ranging from 0 to 5),
- \( p = 0.71 \) (the probability of success on each trial),
- \( \binom{n}{x} \) is the binomial coefficient.
Calculate \( P(x) \) for each value of \( x \) from 0 to 5 and fill in the table, rounding each probability to five decimal places.
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