Question

A large manufacturing firm tests job applicants. Test scores are normally distributed with a mean of 500 and a standard deviation of 50.

-what proportion of people get scores between 400 and 600?

-What proportion of people get higher than 450?

Answer 1

Part a)

P ( 400 < X < 600 )
Standardizing the value

Z = ( 400 - 500 ) / 50
Z = -2
Z = ( 600 - 500 ) / 50
Z = 2
P ( -2 < Z < 2 )
P ( 400 < X < 600 ) = P ( Z < 2 ) - P ( Z < -2 )
P ( 400 < X < 600 ) = 0.9772 - 0.0228
P ( 400 < X < 600 ) = 0.9545

Part b)

P ( X > 450 ) = 1 - P ( X < 450 )
Standardizing the value

Z = ( 450 - 500 ) / 50
Z = -1

P ( Z > -1 )
P ( X > 450 ) = 1 - P ( Z < -1 )
P ( X > 450 ) = 1 - 0.1587
P ( X > 450 ) = 0.8413