Question

You gave a placement test to a group of 150 students whose mathematics ability ranged from very beginning to advanced. The mean of the test scores was 85 with a standard deviation of 12. Approximately what percent of the students scored 85 or below? (Round to the nearest whole percent.)

Answer 1

Explanation:

To find the percentage of students who scored 85 or below on the placement test, we can use the Z-score formula and then look up the corresponding percentage in a standard normal distribution table.

The Z-score formula is:

\[Z = \frac{X - \mu}{\sigma}\]

Where:

- \(X\) is the score we want to find the percentage for (in this case, 85).

- \(\mu\) is the mean (85 in this case).

- \(\sigma\) is the standard deviation (12 in this case).

Now, calculate the Z-score:

\[Z = \frac{85 - 85}{12} = 0\]

A Z-score of 0 means the score is exactly at the mean.

Next, we look up the percentage of scores below a Z-score of 0 in the standard normal distribution table. Since the normal distribution is symmetric, we know that 50% of the scores fall below the mean, and 50% fall above the mean.

Therefore, approximately 50% of the students scored 85 or below on the placement test.