1. **State the problem:** We need to find the percent of curlers aged between 30 and 50, given the ages are normally distributed with mean $\mu=40$ and standard deviation $\sigma=10$. 2. **Recall the empirical rule:** For a normal distribution: - About 68% of data lies within $\pm 1\sigma$ of the mean. - About 95% lies within $\pm 2\sigma$. - About 99.7% lies within $\pm 3\sigma$. 3. **Calculate z-scores for 30 and 50:** $$z_1 = \frac{30 - 40}{10} = -1$$ $$z_2 = \frac{50 - 40}{10} = 1$$ 4. **Interpretation:** The interval 30 to 50 corresponds to $\mu \pm 1\sigma$. 5. **Apply empirical rule:** Approximately 68% of the data lies between $z=-1$ and $z=1$. 6. **Answer for problem 4:** The percent of curlers between 30 and 50 is about 68%. --- 1. **State the problem:** Identify which set (A, B, C, or D) is normally distributed based on the frequency data across intervals. 2. **Recall characteristics of normal distribution:** - Symmetric, bell-shaped distribution. - Frequencies increase to a peak near the mean and then decrease symmetrically. 3. **Analyze each set:** - Set A: Frequencies are 84, 72, 75, 75, 72, 64 — roughly symmetric but not clearly bell-shaped. - Set B: Frequencies are 13, 57, 91, 96, 43, 20 — peak at 96, then sharp drop, somewhat skewed. - Set C: Frequencies are 35, 35, 35, 45, 55, 55 — frequencies increase steadily, no clear peak. - Set D: Frequencies are 64, 48, 38, 72, 55, 87 — irregular, no symmetry or bell shape. 4. **Conclusion:** Set B shows a clear peak near the middle intervals and roughly symmetric decrease, resembling a normal distribution. 5. **Answer for problem 6:** Set B is normally distributed. **Final answers:** - Problem 4: c. 68% - Problem 6: b. Set B