Question

Suppose that the mathematics SAT scores for high school seniors for a specific year have a mean of 456 and a standard deviation of 100 and are approximately normally distributed. If a subgroup of high school seniors with top 1.5 % of students are to be selected to be included in the National Honor Society, what is the minimum score a high school senior must score to be included in the subgroup?

Answer 1

682

Explanation:

mean: 465

standard deviation, sd: 100

value of interest, x: ?

We need to find for which z-score the probability is 1 - 0.015 = 0.985. From the table attached, Z = 2.17

By definition:

Z = (x - mean)/sd

x = Z * sd + mean

x = 2.17 * 100 + 465

x = 682

Then, 682 is the minimum score a high school senior must score to be included in the subgroup