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The mean Exam score on the SOC 15 Exam 2 is 84.28 with a standard deviation of 6.71.You score a 92 on the exam. What percentage of students scored higher than you on the exam?

User Skyork
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First, find the z-score of 92 using the formula


\begin{gathered} z=(x-\mu)/(\sigma) \\ \\ \text{Substitute the following} \\ x=92 \\ \mu=84.28 \\ \sigma=6.71 \end{gathered}
\begin{gathered} z=(x-\mu)/(\sigma) \\ z=(92-84.28)/(6.71) \\ z=(7.72)/(6.71) \\ z=1.15 \end{gathered}

Look for the value of z-score in the z-table

Since we are looking for percentage of higher than 92, subtract 0.87493 from 1


\begin{gathered} P(Z>1.15)=1-0.87493 \\ P(Z>1.15)=0.12507 \end{gathered}

Multiply the result by 100% to get the percentage.


0.12507\cdot100\%=12.507\%

Therefore, the percentage of students who scored higher than you on the exam is 12.507%.

The mean Exam score on the SOC 15 Exam 2 is 84.28 with a standard deviation of 6.71.You-example-1
User Aanu
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