# dolution

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

a. P(Ă˘Ë†â€™2.00 Ă˘â€°Â¤ t10 Ă˘â€°Â¤ 1.00), where t10 has a tĂ‚Â distribution with 10 degrees of freedom.

b. P(Ă˘Ë†â€™2.00 Ă˘â€°Â¤ t 100 Ă˘â€°Â¤ 1.00), where t100 has a tĂ‚Â distribution with 100 degrees of freedom. How do you explain the difference between this result and the one obtained in part a?

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c. P(Ă˘Ë†â€™2.00 Ă˘â€°Â¤ Z Ă˘â€°Â¤ 1.00), where Z is a standardĂ‚Â 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?