I need help with question 3 part d & e please

a) -

b) mean: 1005 and var = 208.334

c) 0.4

3. (20 marks) Let X be the weight of our (in g) contained in a 1kg bag of flour made by a certain company and assume X N U(980, 1030). (a) Draw the graph of the pdf of X. [4 marks] (b) What is the mean and variance of X ? [2 marks] (c) What is the probability that the bag of our has less than 1kg of our in it? [2 marks] (d) If I take 20 bags of flour from the production line today, what is the probability that more than 10 of them will weigh less than 1kg? [Assume the weight of each of them follows the same distribution as above.) [4 marks] (e) The owner of this factory feels that the probability of a bag of our weighing less than 1kg is too high, and adjusts the our dispensing machine to try and reduce this probability. She randomly selects 15 bags of our from the next day's production and 3 of them are found to weigh less than 1kg. Conduct a hypothesis test to decide if there is enough evidence that she has reduced the probability of a bag of our containing less than 1kg. [8 marks] Note: Parts (d) and (e) require you to use the probability from part (c), if for some reason you could not get an answer for part (c) perhaps pretend the answer to part (c) was 0.5. That is not correct but you will get follow on marks