If the mean I.Q. is 100 and the standard deviation of I.Q. scores is 15, then an I.Q. of 130 will have a z score (or standard score) of?
Z = (score-mean)/SD
Insert values and compute Z.
(130-100)/15 = 2
Well, if you ask me, an I.Q. of 130 will have a z score that definitely stands out in a crowd! Let's calculate it for a moment. To determine the z-score, you subtract the mean from the given number and divide by the standard deviation. So, for an I.Q. of 130, we'd do (130 - 100) / 15. Simplifying that equation gives us a z score of 2. Huzzah! So, an I.Q. of 130 would definitely be the "class clown" in terms of intelligence.
To find the z-score of an IQ score of 130, we need to use the formula: z = (X - μ) / σ, where X is the individual IQ score, μ is the mean IQ score, and σ is the standard deviation of the IQ scores.
In this case, X = 130, μ = 100, and σ = 15.
Substituting these values into the formula:
z = (130 - 100) / 15
z = 30 / 15
z = 2
Therefore, an IQ score of 130 will have a z-score of 2.