1. The problem involves calculating the Z-score, which measures how many standard deviations a data point $x$ is from the mean $\mu$. 2. The formula for the Z-score is: $$z = \frac{x - \mu}{\sigma}$$ where: - $x$ is the value from the dataset, - $\mu$ is the mean of the dataset, - $\sigma$ is the standard deviation. 3. Important rules: - A positive Z-score means the value is above the mean. - A negative Z-score means the value is below the mean. - A Z-score of 0 means the value equals the mean. 4. Given the graph with points 5, 7, 8, 9, and 11, and the shaded area between 7 and 9, you can calculate the Z-scores for 7 and 9 if $\mu$ and $\sigma$ are known. 5. For example, if $\mu = 8$ and $\sigma = 1.5$, then: $$z_7 = \frac{7 - 8}{1.5} = \frac{-1}{1.5} = -0.67$$ $$z_9 = \frac{9 - 8}{1.5} = \frac{1}{1.5} = 0.67$$ 6. These Z-scores indicate that 7 is 0.67 standard deviations below the mean, and 9 is 0.67 standard deviations above the mean. 7. The shaded area between these Z-scores represents the probability of a value falling between 7 and 9 in the normal distribution. Final answer: The Z-scores for 7 and 9 are $-0.67$ and $0.67$ respectively, assuming $\mu=8$ and $\sigma=1.5$.