Exercises

Calculate z-scores

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 \( \sigma_X \).

Your task is to calculate the z-score for 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. The z-score for \( x_0 \) gives you the number of standard deviations from \( \mu_X \) that \( x_0 \) is located. Expressed differently, the z-score is the difference between the income \( x_0 \) and the mean income \( \mu_X \) measured in standard deviations.

Before you do this exercise, it is recommended that you are familiar with what standard deviations are and how to calculate them.