The z score for the given x-values is [tex]P(-1.83\le z\le2.33)[/tex]
The formula for calculating the z-score is expressed as:
[tex]z=\frac{x-\mu}{\sigma}[/tex]
First, we need to convert the x-values to z-score:
Given the following:
x = -7.45
Mean = 20
Standard deviation = 15
Substitute into the formula:
[tex]z=\frac{x-\mu}{\sigma}\\z=\frac{-7.45-20}{15}\\z=\frac{-27.45}{15}\\z= -1.83[/tex]
At the other endpoint where x = 54.95;
[tex]z=\frac{54.95-20}{15}\\z=\frac{34.95}{15}\\z=2.33[/tex]
Hene the z score for the given x-values is [tex]P(-1.83\le z\le2.33)[/tex]
Learn more here: https://brainly.com/question/22520030
