Let be the weight of flour (in g) contained in a 1kg bag of flour made by a certain company and assume XU(980,1030) .

(a)Draw the graph of the pdf of X .

(b) What is the mean and variance of X ?

(c)What is the probability that the bag of flour has less than 1kg of flour in it?

(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.)

(e)The owner of this factory feels that the probability of a bag of flour weighing less than 1kg is too high, and adjusts the flour dispensing machine to try and reduce this probability. She randomly selects 15 bags of flour 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 flour containing less than 1kg.