Question

find the z - score for the data point x given mean μ and standard deviation σ. round to two decimal places as needed.
x = 78
μ = 82
σ = 8
show your work here

Explanation:

Step1: Recall z - score formula

The formula for the z - score is $z=\frac{x-\mu}{\sigma}$.

Step2: Substitute given values

Substitute $x = 78$, $\mu = 82$, and $\sigma = 8$ into the formula: $z=\frac{78 - 82}{8}$.

Step3: Calculate the numerator

$78-82=-4$, so $z=\frac{-4}{8}$.

Step4: Simplify the fraction

$\frac{-4}{8}=-0.50$.

Answer:

$-0.50$