Question

In 2012, entering freshmen at the UA have an average ACT score of 25.4 with a standard deviation of 2.1. 1. What is the probability a student has an ACT score more than 24.1

Answer 1

P [ Z > 24,1 ] = 72,24 %

Explanation:

P [ Z > 24,1 ] = 1 - P [ Z < 24,1 ]

P [ Z < 24,1 ] = ( Z - μ₀ ) / σ

P [ Z < 24,1 ] = ( 24,1 - 25,4) / 2,1

P [ Z < 24,1 ] = - 1,3/ 2,1

P [ Z < 24,1 ] = - 0,6190 ≈ - 0,62

We look in z-table and find for z(score) -0,6190

P [ Z < 24,1 ] = 0,27763

Then

P [ Z > 24,1 ] = 1 - 0,27763

P [ Z > 24,1 ] = 0,72237 ⇒ or P [ Z > 24,1 ] = 72,24 %