Statistics assignment
Assignment3 Part 2
(Deadline: Nov 20th 11:59 p.m. EST)
Marks for each part of each question are indicated in parentheses in the questions below.
Please see course outline for Part 2 Marking Scheme for penalties. There are 2 bonus marks (in addition
to the 10 marks indicated below) for putting the answer to this assignment in the PLAN/DO/REPORT
format.
PLAN: (1 bonus mark)
In one or two sentences state the overall business objective.
DO: (no bonus marks, but marks for calculations as asked in the questions)
Do the numerical calculations asked in the question.
REPORT: (1 bonus mark)
Relate the numerical results from “DO” to the business objective given in “PLAN.” One sentence for each
numerical result.
There is no need to lay this out as a table. Three headings PLAN, DO, REPORT are sufficient.
Total marks: 10. This assignment is worth 5% of the course mark.
The maximum grade is 10 marks. If the grade is than 10 marks after adding the bonus marks, the
additional marks will not be carried over.
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 ship’s 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
ship’s 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 ship’s 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) has a cleaning time that is Exponentially distributed with a mean of 8.3
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?