Question

2. Many states have programs for assessing the skills of students in various grades. The Indiana Statewide Testing for Educational Progress (ISTEP) is one such program. In a recent year, 76,531, tenth-grade Indiana students took the English/language arts exam. The mean score was 572 and the standard deviation was 51. Assuming that these scores showed a Normal shape. Use the 68–95–99.7 rule to give a range of scores that includes 95% of these students.

Answer 1

Solution :

Given that,

= 572

= 51

Using Empirical rule,

P( - 2< X < + 2) = 95%

P( 572 - 2 * 51 < X   < 572 + 2 * 51 ) = 95%  

P ( 470 < X < 674 ) = 95%

Range of scores are : 470 and   674