Questions: A population has mean ψ=25 and standard deviation π=5, Round the answers to two decimal places as needed.
(a) Find the z-score for a population value of 8.
The z-score for a population value of 8 is -3.4.
(b) Find the x-score for a population value of 17.
The x-score for a population value of 17 is .
Transcript text: A population has mean $\psi=25$ and standard deviation $\pi=5$, Round the answers to two decimal places as needed.
(a) Find the $z$-score for a population value of 8.
The $z$-score for a population value of 8 is -3.4.
(b) Find the 2 -score for a population value of 17.
The x -score for a population value of 17 is $\square$.
Solution
Solution Steps
Step 1: Given Information
We are provided with the following parameters for the population:
Mean (\( \mu \)) = 25
Standard Deviation (\( \sigma \)) = 5
Step 2: Calculate the z-score for a population value of 17
To find the z-score for a population value of 17, we use the formula:
\[
z = \frac{X - \mu}{\sigma}
\]
Substituting the values into the formula:
\[
z = \frac{17 - 25}{5} = \frac{-8}{5} = -1.6
\]
Final Answer
The z-score for a population value of 17 is \(\boxed{-1.6}\).