Question 3 A certain brand of yogurt is packed in tubs with masses that are normally distributed with mean of 1kg and a standard deviation of 50g. (a) Find the probability that a randomly selected tub weighs i. More than 950g, ii. Between 950g and 1100g. (b) A box contains 20 such tubs. What is the probability that the mean mass for a tub is between 980g and 1030g? Question 4 (a) The production machines of a company produce metal discs of 200g. It is noted that the weight of the discs follows a normal distribution with a standard deviation of 7g. To test the consistency of the machines, 50 discs are randomly selected and the mean weight is 205g. What is the 99% confidence interval for the average weight of the selected discs? (b) A machine produces metal discs with a diameter of 12cm. The diameters of discs need to be exactly 12cm with only a small variation of 2%. On a particular day, the manufacturing manager measured the diameters of 50 discs and noted that the mean is 11.5cm. It is assumed that the diameters of discs are normally distributed with a standard deviation of 1.8cm. Conduct a hypothesis testing using the critical value approach, at the 0.1 level of significance. Is there evidence that the machine is not producing the discs at the specified diameter of 12cm