Question

5. A father who has two children (JD and Sofia) decided to give an award to the child who did best on their math test. JD scored a 57 on his math test while Sofia scored a 32. The dad called the teachers and found that JD's test had a class average of 52.4 with a standard deviation of 6.8 points. Sofia's class had an average of 27.3 and a standard deviation of 5.1. Which kid wins the award? Use Z-scores to justify your answer. Round Z-scores to 2 decimal places.

Answer 1

solution:

JD's score = 57

class average = $\mu$ = 52.4

SD = $\sigma$ = 6.8

so corresponding z score for JD

$z = \frac{X-\mu}{\sigma}=\frac{57-52.4}{6.8}=0.68$

Sofia's score = 32

class average = $\mu$ = 27.3

SD = 5.1

so corresponding z score for sofia

= 32-27.3 5.1 0.92

since z score of sofia is 0.92 which is higher than the z score of JD's 0.68, so relative standing of sofia is higher.

so, sofia will win the award