Question

The College Boards, which are administered each year to many thousands of high school students, are scored so as to yield a mean of 500 and a standard deviation of 100. These scores are close to being normally distributed. An exclusive club wishes to invite those scoring in the top 20% on the College Boards to join.

(a) What score is required to be invited to join the club?

(b) What score separates the top 65% of the population from the bottom 35%?

Answer 1

Answer)

As the data is normally distributed we can use standard normal z table to estimate the answer

Z = (x - mean)/s.d

Given mean = 500

S.d = 100

A)

From z table, p(z>0.84) = 0.2 (20%)

So, 0.84 = (x-500)/100

X = 584

A score of 584 is required

B)

From z table, p(z<-0.39) = 0.35 (35%)

So, -0.39 = (x-500)/100

X = 461