If a distribution of intelligence quotient (IQ) scores has a mean of $100$ and a standard deviation of $15$, an IQ score of $110$ would have a $z$ score of $\frac{110 - 100}{15} = +0.67$. This means the score is approximately two-thirds of a standard deviation above the mean. Conversely, a raw score of $85$ would have a $z$ score of $\frac{85 - 100}{15} = -1.00$, placing it exactly one standard deviation below the mean.