Answer: the minimum score required for the scholarship is 29.24
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