Question

c) the cost of sandals has a mean of $18.30. if the z - score for a $23.70 pair of sandals is 1.8, what is the standard deviation?

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 know that $z = 1.8$, $x=23.70$, and $\mu = 18.30$.

Step2: Rearrange the formula to solve for $\sigma$

Starting from $z=\frac{x - \mu}{\sigma}$, we can cross - multiply to get $z\sigma=x-\mu$, and then $\sigma=\frac{x - \mu}{z}$.

Step3: Substitute the given values

Substitute $x = 23.70$, $\mu=18.30$, and $z = 1.8$ into the formula $\sigma=\frac{x - \mu}{z}$. So, $\sigma=\frac{23.70 - 18.30}{1.8}$.

Step4: Calculate the value of $\sigma$

First, calculate the numerator: $23.70-18.30 = 5.4$. Then, divide by $z$: $\frac{5.4}{1.8}=3$.

Answer:

$3$