Compute the following probabilities:

a. If \(Y\) is distributed \(t_{15}\), find \(\operatorname{Pr}(Y>1.75)\).

b. If \(Y\) is distributed \(t_{90}\), find \(\operatorname{Pr}(-1.99 \leq Y \leq 1.99)\).

c. If \(Y\) is distributed \(N(0,1)\), find \(\operatorname{Pr}(-1.99 \leq Y \leq 1.99)\).

d. Why are the answers to (b) and (c) approximately the same?

e. If \(Y\) is distributed \(F_{7,4}\), find \(\operatorname{Pr}(Y>4.12)\).

f. If \(Y\) is distributed \(F_{7,120}\), find \(\operatorname{Pr}(Y>2.79)\).