Question

Many states assess skills of their students in various grades. One program that is available for this purpose is the NAEP. One of the tests provided by the NAEP assesses the reading skills of 12th grade students. In a recent year, the national mean score was 288 and the standard deviation was 38. Assuming the scores are approximately normal, give a range of scores that includes 99.7% of these students.
Required:
How high a score is needed to be in the top 25% of students who take this exam (use technology)?

Answer 1

Solution :

Given :

National mean score of the reading test that is conducted the NAEP = 288

Standard deviation of the score = 38

Therefore, P(X > x) = 0.25

P (Z > $\frac{x-288}{38}$ = 0.674)

$\frac{x-288}{38} = 0.674$

$x=288+(38 \times 0.674)$

x = 326.67

Therefore, the highest score that is needed for the students to be in the top of 25 percent among the students those who take the exam.