A group of $600$ job applicants is rated on a scale of $1$ to $50$. The ratings have **mean** $32.5$ and **standard deviation** $7.1$. Approximately how many standard deviations above the mean is a rating of $48$?

The number of standard deviations a value $p$ lies from the mean is the **z-score**: $z = \dfrac{p - \text{mean}}{\text{standard deviation}}$. For $p = 48$, mean $= 32.5$, SD $= 7.1$: $z = \dfrac{48 - 32.5}{7.1} = \dfrac{15.5}{7.1} \approx 2.2$. So $48$ is about $2.2$ standard deviations above the mean. - Trap A ($0.5$) is the rough z-score for $36$ — a value much closer to the mean. - Trap B ($1.0$) corresponds to one SD above the mean, which would be $32.5 + 7.1 = 39.6$ — close, but $48$ is further out. - Trap D ($15.5$) treats the *numerator* as the answer, skipping the division by SD.