Entrance exam

In a college entrance exam, the participants are rated as excellent, very good, good, and fair. Consider that the scores in the exam are normally distributed with a mean of 78 and a standard deviation of 7.5. The participants receiving the top 5% of the scores will be rated as excellent, the next 15% as very good, the next 40% as good, and the remaining as fair.

What is the starting score to be rated excellent? (Answer to 2 decimal places. )

Final Answer:

x =  90.34

Step-by-step explanation:

$$\begin{gathered} m=78 \\ \sigma =7.5 \\ z=1.6451 \\ x=m+z\cdot \sigma =78+1.6451\cdot 7.5=90.34 \end{gathered}$$

Use the normal distribution table.

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