Explain the difference in the values of x-y

Question

Solve the below:

Determine the following quantities using Excel:

(a) Find the value of x such that P (t₁₀x › X) = 0.75, where t10 has a t distribution with 10 degrees of freedom.

(b) Find the value of y such that P (t₁₀₀x › X) = 0.75, where t₁₀₀ has a t distribution with 100 degrees of freedom. How do you explain the difference between this result and the result obtained in part a?

(c) Find the value of z such that z P (Z › z) = 0.75, where Z is a standard normal random variable. Compare the results with the results obtained in part a and b. How do you explain the difference in the values of x, y, and z?