Problem 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 (ii) Supposedly you are inserting the above stem-and-leaf display in a report to besubmitted 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:

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 yourconclusion. 

Problem 2

(a) It is noted that 8% of Kaplan students are left handed. If twenty (20) 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. mean and standard deviation for the number of left-handed students

(b) Do you agree that “if two events are mutually exclusive then these two events will be independent”? Why? Provide one business-related example each, with explanation, for mutually exclusive and independent events.