Question 1

a) 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.

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

(b) 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,

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

 (c) 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 2

(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.