Question 1170005
Let's break down this problem step-by-step.

**(a) Probability of Finishing Cleaning Before Cargo Handling:**

1.  **Define Variables:**
    * Let X be the cleaning time for the first side of the ship.
    * Let Y be the cleaning time for the second side of the ship.
    * X ~ N(μx = 9.3, σx = 1.6)
    * Y ~ N(μy = 9.3, σy = 1.6)
    * Correlation coefficient (ρ) = 0.85
    * Cargo handling time = 22.7 hours

2.  **Total Cleaning Time (T):**
    * T = X + Y

3.  **Mean of Total Cleaning Time (μt):**
    * μt = μx + μy = 9.3 + 9.3 = 18.6 hours

4.  **Variance of Total Cleaning Time (σt²):**
    * σt² = σx² + σy² + 2ρσxσy
    * σt² = (1.6)² + (1.6)² + 2(0.85)(1.6)(1.6)
    * σt² = 2.56 + 2.56 + 4.352
    * σt² = 9.472

5.  **Standard Deviation of Total Cleaning Time (σt):**
    * σt = √9.472 ≈ 3.078 hours

6.  **Distribution of Total Cleaning Time:**
    * T ~ N(μt = 18.6, σt = 3.078)

7.  **Calculate the Z-score:**
    * We want to find P(T < 22.7).
    * z = (22.7 - 18.6) / 3.078
    * z = 4.1 / 3.078 ≈ 1.332

8.  **Find the Probability:**
    * P(Z < 1.332) using the standard normal distribution table or a calculator.
    * P(Z < 1.332) ≈ 0.9087

9.  **Conclusion:**
    * The probability that the robot will have finished cleaning the ship's hull before the cargo is offloaded and reloaded is approximately 0.9087 or 90.87%.

**Answer:**

The probability is approximately 0.9087.