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

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?