Question

One year, many college-bound high school seniors in the U.S. took the Scholastic Aptitude Test (SAT). For the verbal portion of this test, the mean was 425 and the standard deviation was 110. Based on this information:

a) What proportion scored 500 or above? Draw the picture!

b) What proportion of the students would be expected to score between 350 and 550? Draw the picture.

Answer 1

Solution :

Given that ,

mean = = 425

standard deviation = = 110

a)

P(x 500) = 1 - P(x   500)

= 1 - P[(x - ) / (500 - 425) / 110]

= 1 -  P(z 0.6818)   

= 1 - 0.7523

= 0.2477

proportion = 0.2477

b)

P(350 < x < 550) = P[(350 - 425)/ 110) < (x - ) /  < (550 - 425) / 110) ]

= P(-0.6818 < z < 1.1364)

= P(z < 1.1364) - P(z < -0.6818)

= 0.8721 - 0.2477

= 0.6244

proportion = 0.6244