IQ scores are measured with a test designed so that the mean is 80 and the stand

Question

IQ scores are measured with a test designed so that the mean is 80 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.) The higher z score boundary is. (Simplify your answer.) What are the IQ scores that separate the unusual IQ scores from those that are usual? The lower bound IQ score is. (Simplify your answer.) The higher bound IQ score is. (Simplify your answer.)

Explanation / Answer

Mean = 80

SD = 16

A) the lower z score boundary = -2

B) the higher z score boundary = 2

C) Z = (X - mean) / SD

Or, -2 = (X - 80)/16

Or, X = 80 - 2*16 = 48

Lower bound IQ score = 48

D) Z = 2

Or, (X - mean)/SD = 2

Or, (X - 80)/16 = 2

Or, X = 80 + 2*16 = 112

Higher bound IQ score = 112

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