1. **Problem Statement:** We are given a normal distribution and need to find the z-score that corresponds to the lowest 23% of the data values and then find the data value associated with that z-score. 2. **Formula and Explanation:** The z-score formula is: $$z = \frac{x - \mu}{\sigma}$$ where $x$ is the data value, $\mu$ is the mean, and $\sigma$ is the standard deviation. The z-score tells us how many standard deviations a data point is from the mean. 3. **Finding the z-score for the lowest 23%:** The lowest 23% corresponds to the 0.23 quantile of the standard normal distribution. Using a z-table or calculator, the z-score for 0.23 cumulative probability is approximately: $$z \approx -0.74$$ 4. **Finding the data value associated with this z-score:** Rearranging the z-score formula to solve for $x$: $$x = z \times \sigma + \mu$$ Since the problem does not provide $\mu$ and $\sigma$, we leave the answer in terms of these variables: $$x = -0.74 \times \sigma + \mu$$ This means the data value at the 23rd percentile is $0.74$ standard deviations below the mean. **Final answers:** - The z-score for the lowest 23% is approximately $-0.74$. - The data value corresponding to this z-score is $x = -0.74 \sigma + \mu$.