INSTRUCTIONS: Caution: 9.01 is tricky because of quirks in the Excel function. Check your answer for reasonableness by comparing it with the answer for the standard normal distribution and with a large value for degrees of freedom.

FACTS: N/A

PROBLEM:

Compute 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 distribution with 10 degrees of freedom. Compare this result to the results obtained in parts (a) and (b). How do you explain the difference 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 one obtained in part (d)?