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The image asks for the area or probability in specific regions of a t-distribution with 16 degrees of freedom. These are calculated using the t-distribution table or using statistical software. I'll calculate each one and round them according to the requirements:

### Given: t-distribution with 16 degrees of freedom.

#### a. To the right of 2.120
We need \( P(T > 2.120) \).
Using a t-distribution table or calculator:
\[
P(T > 2.120) = 0.025
\]

#### b. To the left of 1.337
We need \( P(T < 1.337) \).
Using a t-distribution table or calculator:
\[
P(T < 1.337) = 0.900
\]

#### c. To the left of -1.746
We need \( P(T < -1.746) \).
Since the t-distribution is symmetric, \( P(T < -1.746) = P(T > 1.746) \):
\[
P(T < -1.746) = 0.05
\]

#### d. To the right of 2.583
We need \( P(T > 2.583) \).
Using a t-distribution table or calculator:
\[
P(T > 2.583) = 0.01
\]

#### e. Between -2.120 and 2.120
We need \( P(-2.120 < T < 2.120) \).
This corresponds to \( 1 - 2P(T > 2.120) \):
\[
P(-2.120 < T < 2.120) = 1 - 2(0.025) = 0.950
\]

#### f. Between -1.746 and 1.746
We need \( P(-1.746 < T < 1.746) \).
This corresponds to \( 1 - 2P(T > 1.746) \):
\[
P(-1.746 < T < 1.746) = 1 - 2(0.05) = 0.900
\]

### Summary:
- a: \( P(T > 2.120) = 0.025 \) (to 3 decimals)
- b: \( P(T < 1.337) = 0.90 \) (to 2 decimals)
- c: \( P(T < -1.746) = 0.05 \) (to 2 decimals)
- d: \( P(T > 2.583) = 0.01 \) (to 2 decimals)
- e: \( P(-2.120 < T < 2.120) = 0.95 \) (to 2 decimals)
- f: \( P(-1.746 < T < 1.746) = 0.90 \) (to 2 decimals)

Would you like further details or clarifications on any of these calculations?

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**Relative Questions:**
1. How do we use a t-distribution table for different degrees of freedom?
2. What is the symmetry property of the t-distribution?
3. How does changing degrees of freedom affect the t

For a t-distribution with 16 degrees of freedom, find the area, or probability, in each region:
- To the right of 2.120
- To the left of 1.337
- To the left of -1.746
- To the right of 2.583
- Between -2.120 and 2.120
- Between -1.746 and 1.746

Learn how to calculate probabilities for a t-distribution with 16 degrees of freedom. This guide covers right-tail, left-tail, and two-tailed areas for various t-values, including 2.120, 1.337, -1.746, and 2.583. Perfect for statistics students.

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