Calculate the following probabilities using Excel.PLEASE INCLUDE HOW TO PROGRAM

Question

Calculate the following probabilities using Excel.PLEASE INCLUDE HOW TO PROGRAM THIS IN EXCEL NO JUST THE ANSWERS.
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?

Explanation / Answer

a)

Here we need to use excel function "=TDIST(1.75,10,1)". The answer is

P(t10 1.75) = 0.05534

b)

Here we need to use excel function "=TDIST(1.75,100,1)". The answer is

P(t100 1.75) =0.04159

The difference is due to degree of freedom. In part b, degree of freedom is larger than degree of freedom in part a.

c)

Here we need to use excel function "=1-NORMSDIST(1.75)".

P(Z 1.75) = 0.040059

This part gives probability for standard normal distribution while part a and b gives probability for t-distribution.

d):

Here we need to use excel function "=1-TDIST(0.8,20,1)". The answer is

P(t20 0.80) =0.78344

(e)

Here we need to use excel function "=1-TDIST(0.8,3,1)". The answer is

P(t3 0.80) =0.75890

The difference is due to degree of freedom. In part d, degree of freedom is larger than degree of freedom in part e.

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