Question

According to the CollegeBoard SAT , the 2007 mean SAT math score for students in Tennessee was 550. If Tennessee SAT math scores are normally distributed with a standard deviation of 101, answer the following questions.

1) If a student's SAT math score is in the bottom 20% of scores, what is his/her score?

2) A certain college will only consider appications in which the SAT math score is in the top 12% of scores. What is the minimum score required to be considered?

Answer 1

Given,

= 550 , = 101

We convert this to standard normal as

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

1)

We have to calculate x such that

P (X < x) = 0.20

P( Z < x - / ) = 0.20

From the Z table, z-score for the probability of 0.20 = -0.8416

x - / = -0.8416

x - 550 / 101 = -0.8416

x = 465

b)

We have to calcualte x such that

P (X > x) = 0.12

That is

P( x - / ) = 0.88

From the Z table, z-score for the probability of 0.88 is 1.175

x - / = 1.175

x - 550 / 101 = 1.175

x = 668.675