Author Question: The College Board reported that, in 2014, the mean Math Level 2 SAT subject test score was 686 with ... (Read 58 times)

LaDunn · **on:** Jun 24, 2018

The College Board reported that, in 2014, the mean Math Level 2 SAT subject test score was 686 with a standard deviation of 96 . Assuming scores follow a bell-shaped distribution, use the empirical rule to find the percentage of students who scored less than 494.
a. 97.5
b. 95
c. 2.5

d. 5

Question 2

The College Board originally scaled SAT scores so that the scores for each section were approximately normally distributed with a mean of 500 and a standard deviation of 100 . Assuming scores follow a bell-shaped distribution, use the empirical rule to find the percentage of students who scored less than 400.
a. 16
b. 68
c. 84
d. 32

brbarasa · **Reply #1 on:** Jun 24, 2018

Answer to Question 1

c
RATIONALE: z-score = (494 686)/96 = 2 . Recall that 95 of observations fall within two standard deviations of mean, which means 2.5 of observations fall in each tail. Since we want to know the percentage of students who scored less than 494, we essentially want to know the percentage of observations that fall below 2 standard deviations. 2.5 of observations fall below 2 standard deviations.

Answer to Question 2

a
RATIONALE: z-score = (400 500)/100 = 1 . Recall that 68 of observations fall within one standard deviation of the mean, so 16 of observations will fall in each tail. The percentage of students who scored less than 400 (below 1 standard deviations) is 16.