Let's remake the section 1.4 numerical example, but instead of using the inverse standard normal distribution, employ the inverse Student's T distribution. This means how to find interval limits given the total percentage P(a ≤ z ≤ b) of the population that should be covered by it.

Examples of finding the following quantities:

• Find interval limits [a, b] with that holds 90% of the values that follow a Student's T distribution with parameters T(0, 1).

Another way to see this question is that the b upper limit of the interval [a, b] is chosen in a manner that P(t ≤ b) = 1 − α/2 = 0.95 holds as shown in the next figure.

Example of application on finding inverse Student's T distribution

Use a Python code to find the following quantities:

• Find interval limits [a, b] with that holds 90% of the values that follow a Student's T distribution with parameters T(40, 8): P(a ≤ t ≤ b) = 0.90.