Calculate the following quantities using Excel. (If you have Excel 2010 or later, we suggest using its new functions.)

a. Find the value of x such that P(t10 > x) = 0.75, where t10 has a t distribution with 10 degrees of freedom.

b. Find the value of y such that P(t100 > y) = 0.75, where t100 has a t distribution with 100 degrees­ of freedom. How do you explain the difference­ between this result and the result obtained in part a?

c. Find the value of z such that P(Z > z) = 0.75, where Z is a standard normal random variable. Compare this result to the results obtained in parts a and b. How do you explain the differences in the values of x, y, and z?