Question

a) a market researcher is analyzing the results of a customer survey that ranks a product from 1 to 10. if the mean is 8.5 and the standard deviation is 1.2, find the z - score for the data value of 9.1.

Explanation:

Step1: Recall z - score formula

The z - score formula is $z=\frac{x - \mu}{\sigma}$, where $x$ is the data value, $\mu$ is the mean, and $\sigma$ is the standard deviation.

Step2: Identify values

We are given that $x = 9.1$, $\mu=8.5$, and $\sigma = 1.2$.

Step3: Substitute values into formula

$z=\frac{9.1 - 8.5}{1.2}$.

Step4: Calculate the numerator

$9.1-8.5 = 0.6$.

Step5: Calculate the z - score

$z=\frac{0.6}{1.2}=0.5$.

Answer:

$0.5$