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 statement must be true?
$z_{37}$ is within 1 standard deviation of the mean.
$z_{37}$ is between 1 and 2 standard deviations of the mean.
$z_{37}$ is between 2 and 3 standard deviations of the mean.
$z_{37}$ is more than 3 standard deviations of the mean.

Explanation:

Step1: Recall z - score formula

The z - score is calculated as \(z=\frac{x-\bar{x}}{s}\). Here, assume \(x = 37\), \(\bar{x}=29\) and \(s = 3.6\).

Step2: Calculate the z - score

\(z=\frac{37 - 29}{3.6}=\frac{8}{3.6}\approx2.22\).

Step3: Analyze the result

Since \(1<2.22<2\), Z37 is between 1 and 2 standard deviations of the mean.

Answer:

Z37 is between 1 and 2 standard deviations of the mean.