When a ship arrives in port, an underwater robot cleans the outside of the hull in order to remove sea creatures, seaweed and dirt. The robot has magnetic wheels that allow it to crawl over the ships steel hull. Making the hull smooth in this way can save about 8% of fuel on the next voyage. It is important that the cleaning can be completed before the ship leaves port. (a) (3 marks) The amount of time taken to offload and reload cargo is 22.7 hours. Robot (Type A) cleans one side of the ship followed by the other side. The cleaning time depends on the amount of dirt on the hull and is Normally distributed with a mean of 9.3 hours and a standard deviation of 1.6 hours for one side of the ship. The time for the second side of the ship is also Normally distributed with a mean of 9.3 hours and a standard deviation of 1.6 hours and is correlated with the time taken for the first side with a correlation coefficient of 0.85. What is the probability that the robot will have finished cleaning the ships hull before the cargo is offloaded and reloaded? (b) (3 marks) The amount of time taken to offload and reload cargo depends on the amount of cargo and is Normally distributed with a mean of 22.7 hours with a standard deviation of 2.1 hours. Robot (Type B) cleans both sides of the ship in a time that is Normally distributed with a mean of 19.6 hours and a standard deviation of 2.4 hours. What is the probability that the robot will have finished cleaning the ships hull before the cargo is offloaded and reloaded? Question continued. When the ship arrives at a port empty, it needs to be loaded before departing and it will take 10.5 hours to load. Two robots are used to clean the hull, one on each side. (c) (2 marks) Each robot (Type C) has a cleaning time that is Normally distributed with a mean of 8.3 hours and a standard deviation of 1.2 hours and these times are independent of each other. What is the probability that both sides of the ship will be cleaned in 10.5 hours, ready to depart? (d) (2 marks) Each robot (Type D