Question 1 (Total: 25 marks) The following table shows a recent study on the relationship between gender and interest in Mathematics: Likes Math Does Not TOTALS Like Math Male 100 400 Female 150 TOTALS 250 (a) Complete the table. (3 marks) (b) If a person is randomly selected, what is the probability that the person is male, (2 marks) II. is female and likes Math, (2 marks) III. is male or likes Math? (4 marks) iv. If the person is male, what is the probability that he does not like Math? (5 marks) v. Discuss whether gender and interest in math are independent in this case. (4 marks) (c) Discuss the difference between Quantitative and Qualitative variables. Give an example for each case. (5 marks)Question 2 (Total: 25 marks) (a) A private hospital conducts many operations in a day. From record, 40% of these cases are heart operation. On a particular day, the hospital has 18 operations. Assuming that the number of heart operations follows a binomial distribution, calculate the i. probability that there are 3 heart operations (2 marks) li. probability that there are at most 2 heart operations, (4 marks) ill. mean and standard deviation for the number of heart operations on that day. (4 marks) Iv. In less than 50 words, explain whether it is likely to have 3 or more heart operations on that day? (3 marks) (b) KKF Pizza sold an average of 4 pizzas in an hour. Find the i. probability that exactly 6 pizzas are sold in two hours, (2 marks) il. probability that more than 3 pizzas are sold in an hour, (3 marks) Ill. standard deviation for the number of pizzas sold in an hour. (2 marks) (c) Discuss the differences between discrete and continuous probability distributions