A factory fills its 5 kg bags of rice by setting a timer on an injection machine. It has been found that the weight of rice the machine puts into a bag is normally distributed with standard deviation of 0.1 kg.
(a) If the company wants 99% of all bags to have at least 5 kg as printed on the bag, what mean amount should the injection machine be set to put in each bag?
(b) Using the mean obtained in part (a), find out
(i) the lower and upper boundaries of the middle 50% of bags.
(ii) the minimum volume of the top 2% of bags.