Minimum score required

Question

Suppose ACT Science scores are normally distributed with a mean of 21.2 and a standard deviation of 4.7. A university plans to admit students whose scores are in the

top 35 %. What is the minimum score required for admission? Round your answer to the nearest tenth, if necessary

Answer 1

Given:

𝝁 = 21.2

σ = 4.7

P(x>Z) = 35% = .35

Using the Z-table or Z calculator in the web:

Z = 0.385

Using the formula Z = (x - 𝝁)/σ,

0.385 = (x - 21.2)/4.7

0.385 • 4.7 + 21.2 = x

x ≈ 23.0