Question

Noah got 92 on Exam I in Math 150. The scores of Noah's class have a mean of 81 and astandard deviation of 5.1. Amelia got 88 on Exam I in Math 302. The scores of Amelia'sclass have a mean of 72 and a standard deviation of 4.9. Who is having a relatively highlyscore? Noah or Amelia?

Answer 1

Noah's score = 92

Noah's class mean = 81

Noah's class standard deviation = 5.1

Thus, his z-score his calculated as;

$\begin{gathered} z=\frac{x-\mu}{\sigma} \\ \text{Where }\mu=\operatorname{mean} \\ \sigma=\text{ standard deviation} \end{gathered}$

Thus, for Noahs', we have;

$\begin{gathered} z=\frac{92-81}{5.1} \\ z=\frac{11}{5.1} \\ z=2.1569 \end{gathered}$

Also, similarly for Amelia, we have;

$\begin{gathered} z=\frac{88-72}{4.9} \\ z=\frac{16}{4.9} \\ z=3.2653 \end{gathered}$

From the results above, Amelia's z-score is higher than that of Noah. Thus, Amelia relatively has the higher score.