Question

Among freshman at a certain university, scores on the Math SAT follow a normal curve, with an average of 500 and a standard deviation of 100.
(a) What percentage of students scored above 680?

(b) What score would a student have to earn in order to be at the 75th per- centile of the distribution? The 25th percentile?
(c) What is the interquartile range for this data set?

Answer 1

a) Percentage of scores above 680

= P(X > 680)

= P(z > (680 - 500)/100)

= P(z > 1.8)

= 0.0359

b) z score for 25% bottom area = -0.67

So,

25th percentile = 500 - 0.67*100 = 433

Also,

z score for 25% top area = 0.67

So,

75th percentile = 500 + 0.67*100 = 567

c) Interquartile range = 75th percentile - 25th percentile = 567 - 433 = 134