Question

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

Answer 1

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