Question

Scores for college bound students on the SAT Critical Reading test in recent years follow approximately the Normal (500, 1202) distribution.

10. How high must a student score to place in the top 10% of all students taking the SAT?

11. Suppose we randomly select 4 students. What is the probability their average score is between 400 and 600?

Answer 1

Given that,

mean = = 500

standard deviation = =1202

Using standard normal table,

P(Z > z) = 10%

= 1 - P(Z < z) = 0.10

= P(Z < z ) = 1 - 0.10

= P(Z < z ) = 0.90

= P(Z <1.28 ) = 0.90  

z =1.28 (using standard normal (Z) table )

Using z-score formula  

x = z * +

x= 1.28*1202+500

x= 2038.56

x=2039

(B)

n = 4

= 500

=  / n= 1202 / 4=601

P(400<    <600 ) = P[(400 -500) /601 < ( - ) / < (600 -500) / 601)]

= P(-0.17 < Z < 0.17)

= P(Z <0.17 ) - P(Z <-0.17 )

Using z table

=0.5675 -0.4325

=0.1350

probability= 0.1350