Question

if $\bar{x}=54$ and $s = 12.12$, what is the z - score for 44?
-0.68
-0.46
-0.83
-0.51
-0.57

Explanation:

Step1: Recall z - score formula

The formula for the z - score is $z=\frac{x-\bar{x}}{s}$, where $x$ is the data - point, $\bar{x}$ is the mean, and $s$ is the standard deviation.

Step2: Substitute given values

We are given that $\bar{x} = 54$, $s=12.12$, and $x = 44$. Substitute these values into the formula: $z=\frac{44 - 54}{12.12}$.

Step3: Calculate the numerator

$44-54=-10$. So, $z=\frac{-10}{12.12}$.

Step4: Calculate the z - score

$z\approx - 0.83$.

Answer:

-0.83 (corresponding to the third option in the multiple - choice list)