Question

if the mean temperature of a city is 84.6 with a standard deviation of 3.8, todays z - score is 2.5. what is the temperature today?

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 value from the data set, $\mu$ is the mean, and $\sigma$ is the standard deviation. We want to find $x$. Rearranging the formula gives $x=\mu + z\sigma$.

Step2: Substitute given values

We are given that $\mu = 84.6$, $z = 2.5$, and $\sigma=3.8$. Substitute these values into the formula $x=\mu + z\sigma$. So $x = 84.6+2.5\times3.8$.

Step3: Perform multiplication

First, calculate $2.5\times3.8 = 9.5$.

Step4: Perform addition

Then, calculate $84.6 + 9.5=94.1$.

Answer:

94.1