Question

The mean Exam score on the SOC 15 Exam 2 is 84.28 with a standard deviation of 6.71Your friend scored an 86 on the exam. What percentage of students scored lower than your friendon the exam?

Answer 1

First, find the z-score of 86

`\begin{gathered} z=(x-\mu)/(\sigma) \\ z=(86-84.28)/(6.71) \\ z=(1.72)/(6.71) \\ z=0.2563 \end{gathered}`

Rounding to the nearest hundredth, that is 0.26

Next, find z = 0.26 to the left of z in the z-table and we have the following

Multiply by 100%, and we have

`\begin{gathered} P(z<0.26)=0.60257 \\ \\ 0.60257\cdot100\%=60.257\% \end{gathered}`

Therefore, the percentage of students who scored lower than 86 is 60.257%.