Question

the grades on a history exam were roughly normally distributed with an average of 74 and standard deviation of 5. shane scored a 77 on the exam. find the z - score for shanes exam grade. round to two decimal places as needed. show your work here enter your answer

Explanation:

Step1: Recall z - score formula

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

Step2: Identify values

We have $x = 77$ (Shane's score), $\mu=74$ (mean), and $\sigma = 5$ (standard deviation).

Step3: Substitute values into formula

$z=\frac{77 - 74}{5}=\frac{3}{5}=0.60$

Answer:

$0.60$