Consider the value of t such that the area under the curve between −|t|−|t| and |t||t| equals 0.90.9.  

Step 1 of 2 :  

Select the graph which best represents the given description of t.

To select the graph which best represents the given description of \( t \), we need to understand the scenario where the area under the curve between \(-|t|\) and \(|t|\) equals 0.9. 

### Understanding the Problem
The description states that 90% of the area under the curve of the t-distribution is between \(-|t|\) and \(|t|\). This implies that the remaining 10% of the area is equally split in the tails on either side of the distribution. Thus, each tail will have 5% of the area.

### Key Points
1. The area between \(-|t|\) and \(|t|\) is 0.90.
2. The area in each tail is 0.05.

### Graph Selection
We need a graph that shows the central 90% of the distribution between two symmetric points \(-|t|\) and \(|t|\) on the t-distribution curve, with 5% in each tail.

### Visual Representation
- The x-axis should have two points labeled \(-|t|\) and \(|t|\).
- The area between these points should be shaded to represent 90% of the total area.
- The tails beyond these points should each have 5% of the area.

### Choosing the Graph
We select a graph where:
- The shaded region is symmetric around the mean (center).
- The shaded region encompasses 90% of the total area.
- The tails, each comprising 5% of the area, are outside the shaded region.

If you can provide the options for the graphs, I can help you identify the correct one. Based on the description, we are looking for a graph with the features mentioned above.

Explore how to calculate the area under the t-distribution curve between -|t| and |t|, where 90% of the area lies. This problem involves statistical concepts and the t-distribution formula. Suitable for advanced college-level students and researchers.

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