Question

At a local university, your application will only be considered if you score in the top 75% of all SAT scores (better than at least 25% of the population). You score 428 on your SAT. You know that SAT scores are normally distributed, have µ = 500, and σ = 100. Based on this information, do you need to retake the test? (1 point)

Answer 1

Given,

= 500, = 100

we convert this to standard normal as

P(X < x) = P(Z < x - / )

We have to calculate minimum score X that have to be scored in order to get in top 75%

P( X > x) = 0.75

P(X < x) = 0.25

P(Z < x - / ) = 0.25

From Z table , z-score for the probability of 0.25 = -0.6745

x - / = -0.6745

(x - 500) / 100 = -0.6745

X = 432.55

Since you score 428 which is less than minimum qualification score 432.55,

you need to retake exam,.