The mean Intelligence Quotient (IQ) score is 100, and the standard deviation is 15. Calculate the z-score for Bill Gates' IQ score of 151.45.
To calculate the z-score, we use the formula:
z = (X - μ) / σ
where:
z = z-score
X = Bill Gates' IQ score of 151.45
μ = mean IQ score of 100
σ = standard deviation of 15
Plugging in the values, we get:
z = (151.45 - 100) / 15
z = 51.45 / 15
z = 3.43
Therefore, the z-score for Bill Gates' IQ score of 151.45 is 3.43.