Exercises

Calculate proportions with the normal distribution

In these exercises you have a random variable \( X \) that follows a normal distribution. Our variable \( X \) could be, for instance, the income of a random inhabitant of a country.

You are given the population mean \( \mu_X \), which would be the mean income in the country, and the standard deviation of the income distribution \( \sigma_X \).

You are also given a value that we call \( x_0 \). In our income example, \( x_0 \) would be the income of one inhabitant of the country that we are interested in. Your job is to calculate what proportion who have an income lower than \( x_0 \)

Before you do this exercise, it is recommended that you are familiar with z-scores.