Question 1
a) The following data represent the number of years patients survived after being diagnosed with terminal cancer:
0.4, 0.5, 0.6, 0.6, 0.6, 0.8, 0.8, 0.9, 0.9, 0.9,
1.2, 1.2, 1.3, 1.4, 2.1, 2.4, 2.5, 4.0, 4.5, 4.6
(i) Construct a stem-and-leaf display (6 marks)
(ii) Supposedly you are inserting the above stem-and-leaf display in a report to be submitted to management, write a short comment on the diagram. (4 marks)
b) The following data shows the weight (in kg) of 13 crabs found in a restaurant on a particular evening:
3.4 1.2 1.7 2.4 2.4 1.1 0.9 0.8 1.2 1.6 0.7 1.2 1.3
(i) Compute the mean and median. (3 marks)
(ii) Determine the shape of the distribution based on the sample data. Explain your conclusion. (2 marks)
Question 2
(a) It is noted that 8% of Kaplan students are left handed. If 20 (TWENTY) students are randomly selected, calculate the
i. probability that none of them are left-handed, (2 marks)
ii. probability that at most 2 are left-handed, (3 marks)
iii. standard deviation for the number of left-handed students (2 marks)
(b) If 50 (FIFTY) classes of 20 (TWENTY) students are randomly selected, what is the probability that 10 (TEN) classes have no left-handed students? (3 marks)
Question 3
(a) Superior Construction Pte Ltd successful company dealing with many major projects in Singapore.
Recently, it has submitted its biddings for two major Government projects. Project A worth about $120 million and the company believes it has 40% chance of securing the project. Project B worth $1.8 billion and there is 30% chance the company can win the project. Both projects are independent of each other. What is the probability that the company:
(i) will secure Project A or B but not both
(ii) will not secure Project A or B or will not secure Project B
(iii) A complement and B complement using Venn Diagram
(b) Do you agree that “if two events are mutually exclusive then these two events will be independent”?
Why?
(c) Provide one business- related example each, with explanation, for mutually exclusive and independent events.
