Question

1. the mean price of regular grade gasoline amongst several gas stations in a city is $3.52 with a standard deviation of 0.12. if the gas station closest to mark’s house charges $3.59 for regular gas, what is its z-score? round to the nearest hundredth.

Explanation:

Step1: Recall z - score formula

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

Step2: Identify values

We are given that $x = 3.59$, $\mu=3.52$, and $\sigma = 0.12$.

Step3: Substitute values into formula

Substitute the values into the z - score formula: $z=\frac{3.59 - 3.52}{0.12}$.
First, calculate the numerator: $3.59-3.52 = 0.07$.
Then, divide the numerator by the denominator: $z=\frac{0.07}{0.12}\approx0.5833\cdots$

Step4: Round to nearest hundredth

Rounding $0.5833\cdots$ to the nearest hundredth gives $0.58$.

Answer:

$0.58$