Question

Suppose ACT Reading scores are normally distributed with a mean of 21.4 and a standard deviation of 5.9. A university plans to award scholarships to students whose scores are in the top 9%. What is the minimum score required for the scholarship? Round your answer to the nearest tenth, if necessary.

Answer 1

To find the minimum score required for the scholarship, we need to find the z-score that corresponds to the top 9% of the normal distribution.

Step-by-step explanation:

To find the minimum score required for the scholarship, we need to find the z-score that corresponds to the top 9% of the normal distribution.

Step 1: Convert the top 9% to a z-score using the standard normal distribution table.

Step 2: Use the z-score formula to find the corresponding ACT Reading score.

Step 3: Round the answer to the nearest tenth.

The minimum score required for the scholarship is the score that corresponds to the z-score found in Step 1.