Z scores and probabilities

Question

The honors program at Brad's university only accepts students with an entrance exam score over 400. What percentage of students would be eligible if the students at Brad's school have an average exam score of 250, with a standard deviation of 80

draw normal distribution

Answer 1

μ = 250, σ = 80, and X = 400

This is a normal distribution with the parameters of μ and σ².

Use the z-score formula to find the probability of students accepting into the honors program at Brad's university.

z = (X - μ) / σ = (400 - 250) / 80 = 150/80 = 15/8 ≈ 1.88

P(z > 1.88) = 1 - P(z ≤ 1.88) = 1 - 0.9699 = 0.0301 or 3.01%

About 3.01% of students would be eligible for the honors program at Brad's university.