Question

Many states assess the skills of their students in various grades. One program that is available for this purpose is the National Assessment of Educational Progress (NAEP). One of the tests provided by the NAEP assesses the reading skills of twelfth-grade students. In a recent year, the national mean score was 288 and the standard deviation was 37 . Assume that these scores are approximately Normally distributed, N(288 , 37 ). How high a score is needed to be in the top 25 % of students who take this exam (use technology and give your answer as a whole number)?

Answer 1

Solution:-

Given that,

mean = = 288

standard deviation = = 37

Using standard normal table,

P(Z > z) = 25%

= 1 - P(Z < z) = 0.25  

= P(Z < z) = 1 - 0.25

= P(Z < z ) = 0.75

= P(Z < 0.6745 ) = 0.75  

z = 0.6745

Using z-score formula,

x = z * +

x = 0.6745 * 37 + 288

x = 312.95

x = 313