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Exam scores in a biology class have a normal distribution with a mean of 84 and a standard deviation of 17.4.Would it be unusual for a student to score 120 on this exam?

User Mikelar
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1 Answer

3 votes

Solution

- 68% of the students in the class scored lower than


\begin{gathered} \mu+\sigma \\ \text{where,} \\ \mu=\operatorname{mean} \\ \sigma=\text{standard deviation} \\ \\ \mu+\sigma=84+17.4=101.4 \end{gathered}

- That is, 68% of students scored lower than 101.4

- 95% of the students in the class scored lower than


\begin{gathered} \mu+2\sigma \\ =84+2(17.4) \\ =118.8 \end{gathered}

- This means that 95% of the students scored lower than 118.8

- This implies that roughly 5% of students get a score higher than 118.8.

- 120 is a score that even less that 5% of the students would score, all things being equal.

- Thus, it definitely would be unusual for a student to score 120 on the exam

Final Answer

It would be unusual for a student to score 120 in the exam.

User Sergey Romanov
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