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: Recall the formula for the z - score

The formula for the z - score of a sample mean is \(z=\frac{M-\mu}{\frac{\sigma}{\sqrt{n}}}\), where \(M\) is the sample mean, \(\mu\) is the population mean, \(\sigma\) is the population standard deviation, and \(n\) is the sample size.

Step2: Substitute the given values into the formula

We are given that \(\mu = 200\), \(\sigma=50\), \(n = 25\), and \(M = 220\).
First, calculate \(\frac{\sigma}{\sqrt{n}}\): \(\frac{50}{\sqrt{25}}=\frac{50}{5}=10\).
Then, calculate \(M-\mu\): \(220 - 200=20\).
Now, find \(z\): \(z=\frac{220 - 200}{\frac{50}{\sqrt{25}}}=\frac{20}{10}\).

Answer:

\(z = 2\)