Question

23)Suppose on a certain MTH 101 quiz, you scored a 94%. The mean score in the class was 82.6% with a standard deviation of 12.4%.a)How many standard deviations away from the mean are you?b)Using the following z-table snippet, determine what percent of your classmates you outperformed:

Answer 1

Recall the z score formula:

`z=(x-\mu)/(\sigma)`

The given values are

`x=94,\mu=82.6,\sigma=12.4`

Therefore the score is:

`\begin{gathered} z=(94-86.4)/(12.4) \\ z=0.6129 \end{gathered}`

Therefore the score is 0.6129 standard deviations away from the mean.

b. From the table, the required value is 0.729069

Hence the percentage is 72.9069%