Question

a supervisor finds the mean number of miles that the employees in a department live from work. he finds $\bar{x}=29$ and $s = 3.6$. which mileage is within a z - score of - 1.5?
21 miles
24 miles
36 miles
41 miles

Explanation:

Step1: Recall z - score formula

The z - score formula is $z=\frac{x-\bar{x}}{s}$, where $z$ is the z - score, $x$ is the data point, $\bar{x}$ is the mean, and $s$ is the standard deviation. We want to find $x$ when $z=-1.5$, $\bar{x} = 29$ and $s = 3.6$.

Step2: Rearrange the formula to solve for $x$

Starting from $z=\frac{x - \bar{x}}{s}$, we multiply both sides by $s$: $z\times s=x-\bar{x}$. Then we add $\bar{x}$ to both sides to get $x=\bar{x}+z\times s$.

Step3: Substitute the given values

Substitute $\bar{x} = 29$, $z=-1.5$ and $s = 3.6$ into the formula: $x=29+( - 1.5)\times3.6$.
First, calculate $( - 1.5)\times3.6=-5.4$. Then $x=29 - 5.4=23.6\approx24$.

Answer:

24 miles