Question

1. the mean temperature amongst several major cities on the east coast on a certain day was 68 degrees with a standard deviation of 7.5. if new york city’s z-score was -0.8, what was the temperature that day?

Explanation:

Step1: Recall the z - score formula

The formula for the z - score is $z=\frac{x-\mu}{\sigma}$, where $z$ is the z - score, $x$ is the value we want to find (the temperature in New York City), $\mu$ is the mean, and $\sigma$ is the standard deviation. We know that $z = - 0.8$, $\mu=68$, and $\sigma = 7.5$. We need to solve for $x$.

Step2: Rearrange the z - score formula to solve for $x$

Starting with $z=\frac{x - \mu}{\sigma}$, we can multiply both sides by $\sigma$ to get $z\times\sigma=x-\mu$. Then, we add $\mu$ to both sides to isolate $x$. So the formula becomes $x=\mu+z\times\sigma$.

Step3: Substitute the known values into the formula

Substitute $\mu = 68$, $z=-0.8$, and $\sigma = 7.5$ into the formula $x=\mu+z\times\sigma$. We have $x = 68+(-0.8)\times7.5$.

Step4: Calculate the value of $x$

First, calculate $(-0.8)\times7.5=-6$. Then, $x=68 - 6=62$.

Answer:

62