A machine produces vitamin C tablets, the diameters of which are normally distributed with mean 10mm and standard deviation 0.1mm. A tablet is acceptable if its diameter lies between 9.81mm and 10.19mm. To pass a quality test, at least 90% of the tablets in a pack should be acceptable. (a) Determine the probability that a tablet is acceptable. [5 marks] (b) What is the probability that a pack of 20 tablets will pass the quality test?[6 marks] (c) What is the probability that a pack of 200 tablets will pass the quality test? [9 marks]