1. **State the problem:** We are given a data set with a mean $\mu = 68$ and a standard deviation $\sigma = 4$. We need to find the z-value for the data point $x = 65$. 2. **Formula used:** The z-value (or z-score) is calculated by the formula: $$z = \frac{x - \mu}{\sigma}$$ This formula tells us how many standard deviations a data point is from the mean. 3. **Calculate the z-value:** Substitute the given values into the formula: $$z = \frac{65 - 68}{4} = \frac{-3}{4} = -0.75$$ 4. **Interpretation:** A z-value of $-0.75$ means the data point 65 is 0.75 standard deviations below the mean of 68. **Final answer:** $$z = -0.75$$