A coffee-dispensing machine used in cafeterias is set to dispense coffee with an average fill of 230 ml and a standard deviation of 10 ml per cup. Assume that the volume dispensed is normally distributed.
(a) For a randomly selected cup dispensed by the machine, what is the probability that:
(i) the cup is filled to more than 235 ml?
(ii) the cup is filled to between 235 ml and 245 ml?
(iii) the cup is less than 220 ml full?
(b) If the company supplying the coffee machines wants only 15% of cups to exceed a given fill level, what level of fill (in ml) does this correspond to?
(c) What must the mean fill level (in ml) be set to in order to ensure that no more than 10% of cups are filled to less than 220 ml?