Question

1. the result of a survey that ranks a product from 1 to 10 has a standard deviation of 1.5. if you chose 6 with a z - score of - 1.3, what is the mean score?

Explanation:

Step1: Recall z - score formula

The z - score formula is $z=\frac{x-\mu}{\sigma}$, where $z$ is the z - score, $x$ is the data point, $\mu$ is the mean, and $\sigma$ is the standard deviation.
We are given that $x = 6$, $z=-1.3$, and $\sigma = 1.5$.
We need to solve the formula for $\mu$.

Step2: Rearrange the z - score formula

Starting with $z=\frac{x - \mu}{\sigma}$, we can multiply both sides by $\sigma$: $z\sigma=x-\mu$.
Then, we can rewrite it as $\mu=x - z\sigma$.

Step3: Substitute the given values

Substitute $x = 6$, $z=-1.3$, and $\sigma = 1.5$ into the formula $\mu=x - z\sigma$.
$\mu=6-(-1.3)\times1.5$.
First, calculate $(-1.3)\times1.5=-1.95$.
Then, $\mu=6 + 1.95$.
$\mu = 7.95$.

Answer:

$7.95$