Question

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

Answer:

first find z score for JD

formula is

$z=\frac{x -\mu}{\sigma }$

$z=\frac{57 - 52.4}{ 6.8}$

z= 0.68

z-score for JD is = 0.68

now calculate z score for Sofia

$z=\frac{32 - 27.3 }{ 5.1}$

z= 0.92

z-score for Sofia is = 0.92

z-score shows us how many standard deviation score is away from the mean.

greater z-score means better score.

Sofia's z-score is 0.92 which is greater than z-score of JD of 0.68

hence,

Sofia will win the award,because z-score of Sofia is greater than z-score of JD.