Question 1

a) The following data represent the number of years patients survived after being diagnosed with

terminal cancer

(i) Construct a stem-and-leaf display 

(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.

b) The following data shows the weight (in kg) of 13 crabs found in a restaurant on a particular evening:

(i) Compute the mean and median. (3 marks)

(ii) Determine the shape of the distribution based on the sample data. Explain your

conclusion. 

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, 

ii. probability that at most 2 are left-handed, 

iii. standard deviation for the number of left-handed students

(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?

Question 3

(a) Superior Construction Pte Ltd is a 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 will not secure Project B 

(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

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