Question

Suppose a normal distribution has a mean of six and a standard deviation of 1.5. What is the z-score of x = 5.5?

Short answer

The value of the$z$score is$-0.33$

Step-by-step solution

Given information

Given in the question that, a normal distribution has a mean of six and a standard deviation of 1.5

The value of $x=5.5$

We have to find the value of$z$score

Explanation 

According to the given information,

$X~N(6,1.5)$

Where,

$\mu =6$

$\sigma =1.5$

$x=5.5$

We can compute the $z$score value as follow:

$z=\frac{x-\mu }{\sigma }$

Place the given values in the above equation:

$z=\frac{5.5-6}{1.5}$

$=\frac{-0.5}{1.5}$

$\approx -0.33$