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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:

23Suppose on a certain MTH 101 quiz you scored a 94 The mean score in the class was 826 with a standard deviation of 124aHow many standard deviations away from class=

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SOLUTION

Recall the z score formula:

[tex]z=\frac{x-\mu}{\sigma}[/tex]

The given values are

[tex]x=94,\mu=82.6,\sigma=12.4[/tex]

Therefore the score is:

[tex]\begin{gathered} z=\frac{94-86.4}{12.4} \\ z=0.6129 \end{gathered}[/tex]

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%