Question

IQ scores are measured with a test designed so that the mean is 113 and the standard deviation is 11. Consider the group of IQ scores that are unusual. What are the z scores that separate the unusual IQ scores from those that are​ usual? What are the IQ scores that separate the unusual IQ scores from those that are​ usual? (Consider a value to be unusual if its z score is less than minus2 or greater than​ 2.)

Answer 1

What are the z scores that separate the unusual IQ scores from those that are​ usual?

The lower z score boundary is = –2.

The higher z score boundary is = 2.

What are the IQ scores that separate the unusual IQ scores from those that are​ usual? (Consider a value to be unusual if its z score is less than –2 or greater than​ 2.)

The lower bound IQ score is = (-2*11)+113 = 91.

(lower z score x standard deviation) + mean

The higher bound IQ score is = (2*11)+113 = 135.

(higher z score x standard deviation) + mean