Question

Imagine you take the SAT which has a µ = 500 and σ = 100 and receive a score of X = 600. What proportion of people did better than you?

(round to two decimals)

EXPLAIN HOW YOU GOT THE ANSWER

Answer 1

Solution:

Given: SAT which has a µ = 500 and σ = 100

and you receive a score of X = 600

We have to find proportion of people did better than you.

That is find:

P( X > 600 ) = .............?

Thus find z score for x = 600

Use following z-score formula:

Thus we get:

P( X > 600 ) = P( Z > 1.00 )

P( X > 600 ) =1 - P( Z < 1.00 )

Now look in z table for z = 1.0 and 0.00 and find corresponding area.

P( Z< 1.00 ) = 0.8413

Thus

P( X > 600 ) =1 - P( Z < 1.00 )

P( X > 600 ) =1 - 0.8413

P( X > 600 ) = 0.1587

P( X > 600 ) = 0.16

Thus 0.16 proportion of people did better than you.