Determine whether the following experiment is a binomial experiment. If it is not, state why. A random sample of 75 Cypress College students were asked to disclose what school they plan on transferring to after graduating from Cypress. O This is not binomial since there are more than two outcomes. This is a binomial experiment. This is not binomial since the trials are not independent O This is not binomial since there is not a fixed number of trials

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### Determining a Binomial Experiment

An essential aspect of understanding probability and statistics involves identifying different types of experiments. One common type is the binomial experiment.

**Prompt:**
Determine whether the following experiment is a binomial experiment. If it is not, state why.

**Scenario:**
A random sample of 75 Cypress College students were asked to disclose what school they plan on transferring to after graduating from Cypress.

**Possible Responses:**

- **This is not binomial since there are more than two outcomes.**
- **This is a binomial experiment.**
- **This is not binomial since the trials are not independent.**
- **This is not binomial since there is not a fixed number of trials.**

**Explanation:**

A binomial experiment must satisfy the following criteria:
1. There are a fixed number of trials.
2. Each trial has two possible outcomes: success or failure.
3. The probability of success is the same for each trial.
4. The trials are independent.

**Analysis of the Given Scenario:**
In this case, the students could transfer to multiple different schools, not just two. Therefore, it does not meet the criterion of having only two possible outcomes. Consequently, the correct response would be:

- **This is not binomial since there are more than two outcomes.**

Understanding the characteristics that define a binomial experiment helps in correctly identifying and applying the appropriate statistical methods.
Transcribed Image Text:### Determining a Binomial Experiment An essential aspect of understanding probability and statistics involves identifying different types of experiments. One common type is the binomial experiment. **Prompt:** Determine whether the following experiment is a binomial experiment. If it is not, state why. **Scenario:** A random sample of 75 Cypress College students were asked to disclose what school they plan on transferring to after graduating from Cypress. **Possible Responses:** - **This is not binomial since there are more than two outcomes.** - **This is a binomial experiment.** - **This is not binomial since the trials are not independent.** - **This is not binomial since there is not a fixed number of trials.** **Explanation:** A binomial experiment must satisfy the following criteria: 1. There are a fixed number of trials. 2. Each trial has two possible outcomes: success or failure. 3. The probability of success is the same for each trial. 4. The trials are independent. **Analysis of the Given Scenario:** In this case, the students could transfer to multiple different schools, not just two. Therefore, it does not meet the criterion of having only two possible outcomes. Consequently, the correct response would be: - **This is not binomial since there are more than two outcomes.** Understanding the characteristics that define a binomial experiment helps in correctly identifying and applying the appropriate statistical methods.
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