Distribution with degrees of freedom

Question

1. Consider a t distribution with 27 degrees of freedom. Compute P(<−1.92<t<1.92)
2. . Round your answer to at least three decimal places.
3. Consider a t distribution with 20 degrees of freedom. Find the value of c such that P(t≤c)=0.05
4. . Round your answer to at least three decimal places.

Answer 1

Answers in boldface below. I used RStudio to do the evaluations.

With 27 degrees of freedom, Prob(-1.92 < t < 1.92) = Prob(t < 1.92) - Prob(t < -1.92) = 0.9345

With 20 degrees of freedom, Prob(t ≤ -1.7247) = .05