Question

In Mary's first math test she scored 87%. The mean and standard deviation for the class were 71% and 18% respectively. In her second math test, Mary scored 66%. The mean and standard deviation for the class were 53% and 14% respectively. In which test did Mary do better relative to the rest of the class? Explain your reasoning. (Hint: find the z-scores corresponding to her two test scores.)

Answer 1

Answer:

Step-by-step explanation:

Since your population are the students in math class, you can use the z-score formula $z=(x-\mu)/\sigma$ in order to comparing the two math test scores. Where $\mu$ is the mean for the class, $\sigma$ is the standars deviation and x is Mary score.

For the first test $\mu=.71 , \sigma=.18,x=.87$ , so ,$z_{1} = (.87-.71)/(.18)=.88$.

For the second test $\mu=.53 , \sigma=.14,x=.66$ , so ,$z_{1} = (.66-.53)/(.14)=.93$

Mary do better in the second test, relative to the rest of the class (because  $.88 \leq .93$, it means the second score is nearer to the mean score of the class than the first one )