Question

According to the College Board, scores on the math section of the SAT Reasoning college entrance test for the class of 2010 had a mean of 516 and a standard deviation of 116. Assume that they are roughly normal. A) What was the interval spanned by the middle 68 percent of scores? B) How high must a student score to be in the top 2.5 percent of scores? What are the quartiles of scores from the math section of the SAT Reasoning Test, according to the distribution in Exercise 46?

Answer 1

Solution :

Given that,

mean = = 100

standard deviation = = 15

Using standard normal table,

A ) P(-z < Z < z) = 68%
P(Z < z) - P(Z < z) = 0.68
2P(Z < z) - 1 = 0.68
2P(Z < z ) = 1 + 0.68
2P(Z < z) = 1.68
P(Z < z) = 1.68 / 2
P(Z < z) = 0.84
z = -0.99 and z = 0.99

Using z-score formula,

x = z * +

x = -0.99 * 116 +516

x = 401.16

x = z * +

x = 0.99 * 116 +516

x = 630.84

B ) P( Z > z) = 2.5%

P(Z > z) = 0.025

1 - P( Z < z) = 0..025

P(Z < z) = 1 - 0..025

P(Z < z) = 0.975

z = 1.96

Using z-score formula,

x = z * +

x = 1.96 * 116 +516

x = 743.36