Question

1. sales representatives at a cellular phone retailer sell a mean of \\( \mu = 200 \\) and a standard deviation of \\( \sigma = 50 \\) smartphones per year. at the rochester, new york, branch, \\( n = 25 \\) representatives sell \\( m = 220 \\). compute the \\( z \\)-score for the rochester branch.

Explanation:

Step1: Calculate the standard error

The formula for the standard error $\sigma_M$ is $\sigma_M=\frac{\sigma}{\sqrt{n}}$.
Substitute $\sigma = 50$ and $n = 25$ into the formula:
$\sigma_M=\frac{50}{\sqrt{25}}=\frac{50}{5}=10$

Step2: Calculate the z - score

The formula for the z - score is $z=\frac{M-\mu}{\sigma_M}$.
Substitute $M = 220$, $\mu=200$ and $\sigma_M = 10$ into the formula:
$z=\frac{220 - 200}{10}=\frac{20}{10}=2$

Answer:

$2$