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.)

Question

IQ scores are measured with a test designed so that the mean is 97 and the standard deviation is 16. 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 −2 or greater than​ 2.)

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

The lower z score boundary is __________ ​(Simplify your​ answer.)

Answer 1

Lower boundary z score is -2

x = lower z-score boundary for mean = 97 and standard deviation 16

z = (x - mean)/standard deviation

-2 = (x - 97)/16

x = 16(-2) + 97 = 65

upper boundary would be

x = 16(2) + 97 = 129