ASSUme that a binomial distnbuton w/ a tral repeated n=5 times. Use sore form of techndogy to find the distnbution given the probabilitip=0.717 of sAccess on a gingle trial procedure ulelds a
ASSUme that a binomial distnbuton w/ a tral repeated n=5 times. Use sore form of techndogy to find the distnbution given the probabilitip=0.717 of sAccess on a gingle trial procedure ulelds a
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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Transcribed Image Text:**Title: Understanding Binomial Distribution Through Technology**
**Introduction**
In statistics, a binomial distribution can model the number of successes in a fixed number of trials when the probability of success in each trial is constant. Understanding this concept is essential in various fields, from quality control to medical testing.
**Problem Statement**
Assume that a procedure yields a binomial distribution with a trial repeated \( n = 5 \) times. Use some form of technology to find the distribution given the probability \( p = 0.717 \) of success on a single trial.
**Data Table**
Here's the structure for the binomial distribution where \( x \) is the number of successes and \( P(X = x) \) is the probability of achieving \( x \) successes in 5 trials:
| \( x \) | \( P(X = x) \) |
|--------|---------------|
| 0 | |
| 1 | |
| 2 | |
| 3 | |
| 4 | |
| 5 | |
**Explanation of the Table**
- **\( x \)**: Represents the number of successes in each trial ranging from 0 to 5.
- **\( P(X = x) \)**: Represents the probability of achieving \( x \) successes out of 5 trials. This would typically be filled out using a binomial probability formula or technology such as statistical software or a graphical calculator.
**Using Technology**
To find the distribution:
1. **Statistical Software**: Input the number of trials (n = 5) and the probability of success (p = 0.717). The software will compute the probabilities for each number of successes.
2. **Graphing Calculator**: Use functions for binomial probability distribution with parameters \( n = 5 \) and \( p = 0.717 \).
**Conclusion**
By using technology, we can swiftly determine the probabilities associated with each possible number of successes in a binomial distribution, aiding in better understanding and practical application of statistical concepts.
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