Question

Scores on the ACT college entrance exam are normally distributed with a mean of 21.6 and a standard deviation of 5.3. What percent of scores are between 15 and 25?

Answer 1

To find the percent of scores between 15 and 25 on the ACT exam, calculate the z-scores for both values and use the standard normal distribution table. The area represents the percentage of scores between 15 and 25.

Step-by-step explanation:

To find the percent of scores that are between 15 and 25 on the ACT exam, we need to calculate the z-scores for both values and use the standard normal distribution table.

First, we calculate the z-score for 15:

z = (x - mean) / standard deviation

z = (15 - 21.6) / 5.3

z ≈ -1.245

Next, we calculate the z-score for 25:

z = (x - mean) / standard deviation

z = (25 - 21.6) / 5.3

z ≈ 0.638

Using the standard normal distribution table, we can find the area between -1.245 and 0.638. The area represents the percentage of scores between 15 and 25.