A state administered standardized reading exam is given to eighthgrade students.

Question

A state administered standardized reading exam is given to eighthgrade students. The scores on this exam for all students statewidehave a normal distribution with a mean of 512 and a standard deviation of 70. A local Junior High principal has decided to givean award to any student who scores in the top 10% of statewide scores. How high should a student score be to win thisaward? Give your answer to the nearest integer. 1 How high should a student score be to win thisaward? Give your answer to the nearest integer. 1

Explanation / Answer

Let x.9 be the score on the exam that 10% of allstudents do better than, the 90th percentile point. We know X is normal with =512 and =70. Now Z=(X-)/ is normal with =0 and=1. From normal tables (reading P(Z<.9)) z.9=1.28, hence 1.28+=x.9 1.28(70)+512=601.6=602 1.28(70)+512=601.6=602

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