Question 1 (a) The probabilities that a customer has to wait 2, 3, 4, or 5 minutes at the checkout line are 0.33, 0.25, 0.17, and 0.25 respectively. (i) Construct the probability distribution for this data and sketch the graph. (7 marks) (ii) Find the mean, variance, and standard deviation for the probability distribution. (7 marks) (b) A recent poll of secondary school students found that 30% would ask a school counsellor for help with peer pressure problems. If 14 secondary school students are selected at random, find the probability that (i) Exactly 3 would ask a school counsellor for help with peer pressure problems. (3 marks) (ii) At least 3 would ask a school counsellor for help with peer pressure problems. (5 marks) (iii) Less than 3 would ask a school counsellor for help with peer pressure problems. (3 marks) [Total : 25 Marks]