Question

All of the students at North High School took a benchmark test. When the administration analyzed the students' grades, they found that the grades were normally distributed and that [blank] of the students received grades with z-scores between 0.15 and 0.85.

Answer 1

24.2% students received grades with z-scores between 0.15 and 0.85

Explanation:

We are given the following in the question:

The grades of a benchmark test for North High School were normally distributed.

WE have to find the percentage of students that received grades with z-scores between 0.15 and 0.85.

Formula:

`z_(score) = \displaystyle(x-\mu)/(\sigma)`

P(score between 0.15 < z < 0.85)

`P(0.15 \leq z \leq 0.85)\\\\= P(z \leq 0.85) - P(z \leq 0.15)\\\\\text{Calculating the value from standard normal z-table}\\\\= 0.802 - 0.560 = 0.242 = 24.2\%`

24.2% students received grades with z-scores between 0.15 and 0.85