10.1k views
1 vote
A two-year college will accept any student ranked in the top 25% on a state exam. If the test score is normally distributed with a mean of 500 and a standard deviation of 100, what is the cut-off score for acceptance?a) 480b) 625c) 567d) 500

1 Answer

4 votes

We need o find the cut-off score for acceptance.

We know that the scores are normally distributed with a mean of 500 and a standard deviation of 100.

Thus, we can use a z-score table to find Z for which the percentage above it is 25% = 0.25.

Then, we calculate the cut-off score x as follows:


z=\frac{x-\text{ mean}}{\text{ standard deviation}}

Using a z-score table, we find the the z with a percentage above 0.25 (one minus the percentage below 0.75) is:


z\cong0.674

Then, we obtain:


\begin{gathered} 0.674=(x-500)/(100) \\ \\ 67.4=x-500 \\ \\ x=67.4+500 \\ \\ x=567.4 \\ \\ x\cong567 \end{gathered}

Answer: c) 567

User Pawlik
by
8.0k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories