Question

GMAT scores for students accepted to Suffolk University’s MBA program are approximately normally distributed with a mean score of 465 and a standard deviation of 103.

a. What score does a student need to have to be at the 85th percentile? Do not round.

b. What is the probability that an accepted student has a GMAT score between 400 and 500? Round z-values to 2 decimal places.

Answer 1

Given that,

mean = = 465

standard deviation = = 103

Using standard normal table,

P(Z < z) =85 %

= P(Z < z) = 0.85  

= P(Z <1.04 ) = 0.85

z =1.04 Using standard normal z table,

Using z-score formula  

x= z * +

x= 1.04 *103+465

x= 572.12

(B)

P(400< x <500 ) = P[(400-465) /103 < (x - ) / < (500-465) /103 )]

= P( -0.63< Z <0.34 )

= P(Z <0.34 ) - P(Z < -0.63)

Using z table   

= 0.6331-0.2643

probability= 0.3688