11. sales representatives at a cellular phone retailer sell a mean of \\( \\mu = 200 \\) and a standard…

11. 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.

11. 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.

Answer

Explanation:

Step1: Recall the formula for the z - score of a sample mean

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{\sigma}{\sqrt{n}}=\frac{50}{\sqrt{25}}=\frac{50}{5} = 10). Then, calculate (z): (z=\frac{220 - 200}{10}).

Step3: Simplify the expression

(z=\frac{20}{10}=2).

Answer:

(2)