Question

12. Kyle and Ryan take entrance exams at two different universities. Kyle scores a 480 on an exam with a mean of 400 and a standard deviation of 68, while Ryan scores a 42 on an exam with a mean of 31 and a standard deviation of 2. Which do you think is more likely to be accepted at the university of his choice?RyanKyle

Answer 1

The first thing is to find the Z- score of both of them

Kyle scores a 480 on an exam with a mean of 400 and a standard deviation of 68,

$Z=\frac{data\text{ value -mean}}{\text{standard deviation}}$$Z=\text{ }\frac{480-400}{68}$$\begin{gathered} Z=\text{ }\frac{80}{68} \\ Z=1.17647 \end{gathered}$

Ryan scores a 42 on an exam with a mean of 31 and a standard deviation of 2.

$\begin{gathered} Z=\frac{42-31}{2} \\ \\ Z=\frac{11}{2} \\ \\ Z=\text{ 5.5} \end{gathered}$

Since , Ryan Z score is higher, Ryan would be accepted at the university of his choice