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An IQ test has a mean of 97 and a standard deviation of 5. Which is...

An IQ test has a mean of 97 and a standard deviation of 5. Which is more​ unusual, an IQ of 107 or an IQ of 84​?

An IQ of _____is more unusual because its corresponding​ z-score, ________

is further from 0 than the corresponding​ z-score of _______ for ________.

Math   Statistics-And-Probability   
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Answer #1

If a random Variable X has mean and standard deviation   , then the Z score for any value of X is =

Here , = 97 and = 5

For , X = 107 , Z =(107-97)/5 = 2

For, X = 84 , Z = (84-97)/2 = -2.6

We know for any observation Z score should be close to 0 to be a usual observation.

Here an IQ of 84 is more unusual because it's corresponding Z score -2.6 is further from 0 than the corresponding Z score of 2 for 107

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