1. **State the problem:** We are given a raw score $X=95$, a Z-score $Z=-1.5$, and a mean $\mu=110$. We need to find the standard deviation $\sigma$ of the normal distribution. 2. **Recall the formula for Z-score:** $$Z=\frac{X-\mu}{\sigma}$$ This formula relates the raw score, mean, standard deviation, and Z-score. 3. **Substitute the known values:** $$-1.5=\frac{95-110}{\sigma}$$ 4. **Simplify the numerator:** $$-1.5=\frac{-15}{\sigma}$$ 5. **Solve for $\sigma$ by multiplying both sides by $\sigma$ and dividing both sides by $-1.5$:** $$\cancel{-1.5} \times \sigma = \frac{-15}{\cancel{\sigma}} \times \sigma \Rightarrow -1.5\sigma = -15$$ $$\frac{\cancel{-1.5}\sigma}{\cancel{-1.5}} = \frac{-15}{\cancel{-1.5}} \Rightarrow \sigma = 10$$ 6. **Interpretation:** The standard deviation of the distribution is 10. **Final answer:** $$\boxed{10}$$