1. **Problem 1: Probability of exceeding 13,000 steps** The number of steps per day is normally distributed with mean $\mu=10000$ and standard deviation $\sigma=1500$. We want to find the percentage of days the student exceeds 13,000 steps, i.e., $P(X>13000)$. 2. **Formula and approach:** Use the standard normal distribution $Z=\frac{X-\mu}{\sigma}$. Calculate the z-score for 13,000 steps: $$z=\frac{13000-10000}{1500}=\frac{3000}{1500}=2$$ 3. **Find the probability:** From standard normal tables or using symmetry: $$P(X>13000)=P(Z>2)$$ The area to the right of $z=2$ is approximately 0.0228 or 2.28%. 4. **Interpretation:** This means the student exceeds 13,000 steps about 2.28% of the days. --- 5. **Problem 2: Probability of obtaining two heads and one tail when tossing three coins** 6. **Total outcomes:** Each coin has 2 outcomes, so total outcomes for 3 coins: $$2^3=8$$ 7. **Favorable outcomes:** Number of ways to get exactly two heads and one tail is the number of ways to choose which 2 coins are heads: $$\binom{3}{2}=3$$ 8. **Probability:** $$P=\frac{3}{8}$$ 9. **Interpretation:** The probability of getting exactly two heads and one tail is $\frac{3}{8}$. --- **Final answers:** - Probability of exceeding 13,000 steps: 2.28% - Probability of two heads and one tail in three coin tosses: $\frac{3}{8}$