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

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**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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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. --- This text is tailored to appear on an educational website, presenting the problem statement, table, and method to solve it clearly and concisely.
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