# Probability and Degrees of Freedom Analysis with Excel

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)?

[PLEASE FIND AN EXCEL SPREAD SHEET WITH THE PROBLEM AND ANY NECESSARY DATA ATTACHED AS AN ATTACHMENT]

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#### Solution Preview

Please see the attached spreadsheet for explanation and formulas.

using excel functions the follwing probabilities are calculated

(a) P (t10 ≥ 1.75) = 0.055340472

By using TDIST(X, degrees of freedom , ...

#### Solution Summary

Probability and degrees of freedom analysis are analyzed by using excel. A t distribution is used.