a supervisor finds the mean number of miles that the employees in a department live from work. he finds…

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?\n$z_{37}$ is within 1 standard deviation of the mean.\n$z_{37}$ is between 1 and 2 standard deviations of the mean.\n$z_{37}$ is between 2 and 3 standard deviations of the mean.\n$z_{37}$ is more than 3 standard deviations of the mean.

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?\n$z_{37}$ is within 1 standard deviation of the mean.\n$z_{37}$ is between 1 and 2 standard deviations of the mean.\n$z_{37}$ is between 2 and 3 standard deviations of the mean.\n$z_{37}$ is more than 3 standard deviations of the mean.

Answer

Explanation:

Step1: Recall z - score formula

The z - score formula is $z=\frac{x-\bar{x}}{s}$, where $x$ is the data - point, $\bar{x}$ is the mean, and $s$ is the standard deviation. Here, $\bar{x} = 29$, $s = 3.6$, and $x = 37$.

Step2: Calculate the z - score

Substitute the values into the formula: $z=\frac{37 - 29}{3.6}=\frac{8}{3.6}\approx2.22$.

Step3: Analyze the z - score range

Since $2<2.22<3$, the z - score $z_{37}$ is between 2 and 3 standard deviations of the mean.

Answer:

$z_{37}$ is between 2 and 3 standard deviations of the mean.