Question

The range of an SAT test is 400-1,600. On average, test-takers score 1,050 with a standard deviation of 195. What are the probabilities for the following scenarios:

i) obtaining a score of 1,400 or more

ii) obtaining a score between 1,200 and 1,400

iii) obtaining a score less than 800

Answer 1

Given,

= 1050 , = 195

We convert this to standard normal as

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

a)

P( X >= x) = 1400 - 1050 / 195)

= P( Z >= 1.7949)

= 0.0363

b)

P( 1200 < X < 1400) = P( X < 1400) - P( X < 1200)

= P (Z < 1400 - 1050 / 195) - P( Z < 1200 - 1050 / 195)

= P( Z < 1.7949) - P( Z < 0.7692)

= 0.9637 - 0.7791

= 0.1846

c)

P( X < 800) = P( Z < 1050 - 800 / 195)

= P( Z < 1.2821)

= 0.9001