Question

Suppose ACT Science scores are normally distributed with a mean of 20.8 and a standard deviation of 5.2. A university plans to send letters of recognition to students whose scores are in the top 12%. What is the minimum score required for a letter of recognition? Round your answer to the nearest tenth, if necessary.

Answer 1

Hello,

Answer 26.9

Explanation:

`z=(x-m)/(\sigma) \\m=20.8\\\sigma=5.2\\\\p(z>?)\geq 0.12\ \longrightarrow 1-p(z\leq ?)=(1-0.12))\\\\Using\ table\ of\ normal\ reduce\ with\ 4 \decimals : ?=1.175\\\\x=1.175*5.2+20.8=26.91\approx{26.9}`