Calculate the following probabilities using Excel.
a. P(t10 ≥ 1.75), where t10 has a t distribution with 10 degrees of freedom.
b. P(t100 ≥ 1.75), 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(Z ≥ 1.75), 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 these probabilities?
d. P(t20 ≤ 0.80), where t20 has a t distribution with 20 degrees of freedom.
e. P(t3 ≤ 0.80), where t3 has a t distribution with 3 degrees of freedom. How do you explain the difference between this result and the result obtained in part d?