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 38 . Assume that these scores are approximately Normally distributed, N(288 , 38 ). use the 68-95-99.7 rule to give a range of scores that include 95% of these students

Answer 1

Answer)

According to the emperical rule

If the data is normally distributed

Then 68% lies in between mean - s.d and mean + s.d

95% lies in between mean - 2*s.d and mean + 2*s.d

99.7% lies in between mean - 3*s.d and mean + 3*s.d

Given mean = 288

S.d = 38

So, 95% lies in between 288 - (38*2) and 288 + (38*2)

That is in between 212 and 364