(a) A manager at a local hospital learnt that during the Friday peak period of 8.00 a. m. – 9.00 a. m. there were, on average, three operations carried out in Ward A. Calculate the probability that on a particular Friday between 08.00 a. m. and 09.00 a. m.: (i) There are three to five operations carried out in Ward A. (5 marks)

(ii) There are at least two operations carried out in Ward A. (5 marks)

(iii) Calculate the standard deviation for this distribution. (1 mark)

(b) A professional basketball player scores 85% of the free throws he tries. Assuming this percentage will hold true for future attempts:

(i) Find the probability that in the next random eight (8) tries, the number of free throws he will score ranges from six to nine. (7 marks)

(ii) Describe the shape of the distribution. Justify your answer.