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The problem asks you to find the probability \( P(T > 2.42) \) for a t-distribution with 12 degrees of freedom.

To solve this:

1. We need to find the cumulative probability for the t-value \( T = 2.42 \) using the t-distribution table or a calculator.
2. We will subtract this cumulative probability from 1 to get \( P(T > 2.42) \).

### Steps:

- Use a t-distribution table or a calculator that can handle t-distributions to find \( P(T \leq 2.42) \) for 12 degrees of freedom.
- Once you have the value \( P(T \leq 2.42) \), subtract it from 1:
  
  \[
  P(T > 2.42) = 1 - P(T \leq 2.42)
  \]

### Using a calculator or a tool like Excel:
You can calculate this value using an online t-distribution calculator or software like Excel. In Excel, you would use:
```excel
=TDIST(2.42, 12, 1)
```
This will give you the one-tailed p-value for \( P(T > 2.42) \).

Would you like a detailed breakdown of these calculations or further clarification?

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Here are 5 related questions:
1. What is a t-distribution, and when is it used instead of a normal distribution?
2. How do you calculate probabilities using a t-distribution table manually?
3. What is the relationship between degrees of freedom and the shape of the t-distribution?
4. How do you interpret the p-value in the context of hypothesis testing?
5. How does the result change if we change the degrees of freedom?

**Tip**: Remember, the larger the degrees of freedom, the closer the t-distribution approximates the normal distribution.

Consider a t-distribution with 12 degrees of freedom. Find P(T > 2.42).

Learn how to find the probability P(T > 2.42) for a t-distribution with 12 degrees of freedom. This example demonstrates how to use the t-distribution table or calculator, involving the key formula P(T > 2.42) = 1 - P(T ≤ 2.42). Suitable for college-level students.

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