Question

4. IQ scores are measured with a test designed so that the mean is 105 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 minus−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 ___

The higher z score boundary is____

What are the IQ scores that seperate the unusual IQ scores from those that are usual?

The lower bounds IQ scores is ___

The higher bounds IQ scores is ____

Answer 1

Given that, mean $(\mu)$ = 105 and standard deviation $(\sigma)$ = 16

the z-scores that seperates the unusual IQ scores from those that are usual.

The lower z score boundary is -2

The higher z score boundary is +2

IQ score corresponding z score = -2 is,

$X = z\sigma + \mu = (-2 * 16) + 105 = -32 + 105 = 73$

IQ score corresponding z score = 2 is,

$X = z\sigma + \mu = (2 * 16) + 105 = 32 + 105 = 137$

Therefore,

The lower bound IQ score is 73

The higher bound IQ score is 137