Suppose ACT Reading scores are normally distributed with a mean of 21 and a standard deviation of 6.1. A university plans to award scholarships to students whose scores are in the top 9%. What is the minimum score required for the scholarship?

Answer: the minimum score required for the scholarship is 29.24

Step-by-step explanation:

Since the scores are normally distributed, it follows the central limit theorem. The formula for determining the z score is

z = (x - µ) / σ

Where

x = sample mean

µ = population mean

σ = population standard deviation

Since the university plans to award scholarships to students whose scores are in the top 9%, the scores that would be qualified are scores which are at least 91% (100 - 9 = 91).

Looking at the normal distribution table, the z score corresponding to the probability value of 0.91 (91/100) is 1.35

From the information given,

µ = 21

σ = 6.1

Therefore,

1.35 = (x - 21) / 6.1

6.1 * 1.35 = x - 21

8.235 = x - 21

x = 8.235 + 21 = 29.24