Question 3 (Total: 25 marks) The weight of a tub of ice-cream from a certain brand is normally distributed with mean of 250g and a standard deviation of 30g. (a) If a tub of ice-cream is randomly selected, I. What is the probability that its weight is more than 260g? (3 marks) Il. What is the probability that its weight is between 225g and 270g? (4 marks) Ill. If 20% of the tubs is above a certain weight W, find the value of W. (5 marks) (b) A box contains 6 such tubs of ice-cream. What is the probability that the mean weight is between 230g and 275g? (8 marks) (c) Explain what is "sampling distribution of sample mean". (5 marks)Question 4 (Total: 25 marks) (a) The bottling machines of a company fill up cans with cherry soda drink to a volume of about 350 ml. It is noted that the volume in each can of soda follows a normal distribution. To test the consistency of the machines, 20 cans are randomly selected and the mean volume is 355 m/ while the standard deviation is 16 ml. (1) What is the 95% confidence interval for the average volume of the selected cans? (6 marks) (1) With reference to this context, explain the meaning of the confidence interval that you have obtained. (6 marks) (b) A company claims that the standby time for its new model of mobile phone is at least 46 hours. A sample of 20 phones yielded a mean standby time of 44 hours and standard deviation of 2.8 hours. It is assumed that the standby time is normally distributed. Conduct a hypothesis testing using the critical value approach, at the 0.05 level of significance. Is there evidence that the mean standby time as claimed by the company is true? (13 marks)