Question

If a random variable is distributed N(9, 1), and a random

realization of it is 3 , find the z-score of 3.

Answer 1

The z-score of a value of 3, for a normal distribution with mean 9 and standard deviation 1, is found to be -6, indicating it is 6 standard deviations below the mean.

Step-by-step explanation:

To calculate the z-score for a random realization of a variable that is normally distributed with a mean (μ) of 9 and a standard deviation (σ) of 1, when the observed value (x) is 3, we use the following formula:

z = (x - μ) / σ

Substitute the given values into the formula:

z = (3 - 9) / 1

z = -6 / 1

z = -6

This means that the value of 3 is 6 standard deviations below the mean in this normal distribution.