Calculate the following quantities using Excel.
a. P(-2.00 ≤ t10 ≤ 1.00), where t10 has a t distribution with 10 degrees of freedom.
b. P(-2.00 ≤ t100 ≤ 1.00), where t100 has a t distribution with 100 degrees of freedom. How do you explain the difference between this result and the one obtained in part a?
c. P(-2.00 ≤ Z ≤ 1.00), 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 these probabilities?
d. Find the 68th percentile of the t distribution with 20 degrees of freedom.
e. Find the 68th percentile of the t distribution with 3 degrees of freedom. How do you explain the difference between this result and the result obtained in part d?