Question

the running times for the 100 are posted by the ohs track team is normally distributed with a mean time 13.4 seconds with a standard deviation of 1.6 sec. find the z - score of a player who ran a 9.6.

Explanation:

Step1: Recall z - score formula

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

Step2: Identify values

We have $x = 9.6$, $\mu=13.4$, and $\sigma = 1.6$.

Step3: Substitute values into formula

$z=\frac{9.6 - 13.4}{1.6}=\frac{- 3.8}{1.6}=-2.375$

Answer:

$-2.375$