11. Sales representatives at a cellular phone retailer sell a mean of \( \mu=200 \) and a standara smartphones per year. At the Rochester, New York, branch, \( n=25 \) representatives sell \( M=220 \). Compute the \( z \)-score for the Rochester branch. 12. A sample of \( n=64 \) scores has a mean of \( M=68 \). Assuming that the population mean is \( \mu=60 \), find the \( z \)-score for this sample: a. If it was obtained from a population with \( \sigma=16 \) b. If it was obtained from a population with \( \sigma=32 \)

To compute the \( z \)-score for the Rochester branch, we can use the formula: \[ z = \frac{M - \mu}{\sigma / \sqrt{n}} \] First, we need to calculate the standard deviation for the population which isn't provided, but if we denote it with \( \sigma \), we can write the formula as follows. Assuming that the population standard deviation is \( \sigma \), the \( z \)-score becomes: \[ z = \frac{220 - 200}{\sigma / \sqrt{25}} = \frac{20}{\sigma / 5} = \frac{100}{\sigma} \] Now, without \( \sigma \), we can't get a numerical answer, but you see how it works! For the second part of your query, you need to calculate \( z \)-scores with given population means and standard deviations. Here’s how you approach both scenarios: a. For \( \sigma=16 \): \[ z = \frac{68 - 60}{16 / \sqrt{64}} = \frac{8}{2} = 4 \] b. For \( \sigma=32 \): \[ z = \frac{68 - 60}{32 / \sqrt{64}} = \frac{8}{4} = 2 \] So, in summary, the \( z \)-score indicates how many standard deviations away the sample mean is from the population mean!