(a) Find the t-value such that the area in the right tail is 0.20 with 17 degrees of freedom. (Round to three decimal places as needed.)

Step 1 ：We are given that the area in the right tail is 0.20 and the degrees of freedom is 17.

Step 2 ：We need to find the t-value for these given conditions.

Step 3 ：The cumulative probability is calculated as 1 minus the area in the right tail, which is \(1 - 0.20 = 0.80\).

Step 4 ：Using the t-distribution table or a function that can calculate the t-value for a given area under the curve and degrees of freedom, we find that the t-value is approximately 0.863.

Step 5 ：\(\boxed{0.863}\) is the t-value such that the area in the right tail is 0.20 with 17 degrees of freedom.