1. **State the problem:** Find the probability that a randomly chosen person scored between 100 and 120 on a test where scores are normally distributed with mean $\mu=117$ and standard deviation $\sigma=9.4$. 2. **Formula and rules:** The probability that a value $X$ lies between $a$ and $b$ in a normal distribution is given by: $$P(a < X < b) = P\left(\frac{a-\mu}{\sigma} < Z < \frac{b-\mu}{\sigma}\right)$$ where $Z$ is the standard normal variable with mean 0 and standard deviation 1. 3. **Calculate z-scores:** $$z_1 = \frac{100 - 117}{9.4} = \frac{-17}{9.4} = -1.8085$$ $$z_2 = \frac{120 - 117}{9.4} = \frac{3}{9.4} = 0.3191$$ 4. **Find probabilities from z-table or standard normal CDF:** $$P(Z < -1.8085) \approx 0.0353$$ $$P(Z < 0.3191) \approx 0.6255$$ 5. **Calculate the probability between 100 and 120:** $$P(100 < X < 120) = P(Z < 0.3191) - P(Z < -1.8085) = 0.6255 - 0.0353 = 0.5902$$ 6. **Interpretation:** There is approximately a 59.02% chance that a randomly chosen person scored between 100 and 120. **Final answer:** $$\boxed{0.5902}$$