Find the t-value such that the area in the right tail is 0.05 with 20 degrees of freedom.

Step 1 ：We are given that the area in the right tail is 0.05 and the degrees of freedom is 20. We are asked to find the t-value.

Step 2 ：The t-value is a value that allows us to make decisions in a t-test. It's calculated from the sample data using a formula. However, in this case, we are asked to find the t-value given the area in the right tail (0.05) and the degrees of freedom (20). This is a reverse lookup problem.

Step 3 ：We can solve this problem by using the inverse of the cumulative distribution function (CDF), also known as the percent-point function (PPF). The PPF gives the value of the variable given a probability.

Step 4 ：By using the PPF, we find that the t-value is approximately 1.7247182429207857.

Step 5 ：Final Answer: The t-value such that the area in the right tail is 0.05 with 20 degrees of freedom is approximately \(\boxed{1.725}\).