1. (a) A coffee dispensing machine is set to discharge on the average 245 ml of coffee into 250 ml cups. Suppose the amount of coffee dispensed is normally distributed with a standard deviation of 7 ml. i. Find the proportion of cups that will be overfilled. (3 marks] ii. Determine the size of the cup that should be used so that not more than 5% cups will overflow. [3 marks] iii. The coffee is sold at $25 per cup. However, the dispenser owner promises $5 refund if a cup contains less than 235 ml coffee. Suppose the cost of coffee is $15 per cup, find the owner's expected profit per cup. [4 marks]