For a t distribution with 16 degrees of freedom, find the area, or probability, in each region.
a. To the right of 2.120. (Use 3 decimals.)
0.025
To find the area to the right of 2.120 in a t-distribution with 16 degrees of freedom, we can use a t-table or a statistical calculator. I'll explain how to use a t-table.
1. Look up the critical value in the t-table. Since we want to find the area to the right of 2.120, we need to find the cumulative probability (area) to the left of 2.120 and then subtract it from 1.
The degrees of freedom is 16. In the t-table, find the row that corresponds to 16 degrees of freedom.
2. Locate the column that contains the value 2.120 or the closest value to it.
3. Read the cumulative probability (area) in that cell. This represents the area to the left of 2.120.
For example, let's say the cumulative probability to the left of 2.120 is 0.975.
4. Subtract the cumulative probability from 1 to find the area to the right of 2.120.
Area to the right of 2.120 = 1 - 0.975 = 0.025
Therefore, the area to the right of 2.120 in a t-distribution with 16 degrees of freedom is approximately 0.025.