Problem 2 (16 marks in total). Goodtaste Ltd , a coffee manufacturer, has recently been prosecuted for selling an underweight 100 g jar of coffee. You have been asked to give assistance to the quality control manager who is investigating the problem. Jars are filled automatically and the filling machine can be preset to any desired weight. For the 100 g jars of coffee, a weight of 101 g is set. There is no subsequent checking of the weight of individual jars, although samples are occasionally taken to check for quality. The standard deviation will depend to a certain extent on the mean weight, but for weights between 90 g and 110 g, it is virtually constant at 1.5 g. You have been asked to apply your knowledge of the normal distribution to the problem. In particular, you have been told that prosecution only occurs when the product is underweight by more than 2%, so you need to find the probability that such a weight could happen by chance. (a) Assuming that the mean weight is 101 g, what proportion proportions of jars are: (i) (3 marks) under 100 g in weight? (ii) (3 marks) over 100 g in weight? (iii) (5 marks) within 2 g of the marked weight? (b) (5 marks) What should the mean weight be set to in order that the probability of a jar weighing less than 98 g is less than 0.1%