Anna is the owner of Novril a food distribution companv. Novril receives large quantities of beans, broccoli and asparagus from local M producers which it processes and packs in bags. In his factorv, onlv one machine is used to pour vegetables into labeled bags of 6 kg. The weight of the vegetables that It mav obvioushmlI varyr somewhat from bag to bag. The machine is now available from such that the weight of the bags of vegetables is distributed according to a normal distribution of mean u = 6.4- kg and standard deviation o' = (13 kg. We l'l therefore assume that the quantitv ofvegetables poured into a bag is independent of it in an1..lI other bag. 1] What proportion of bags weigh less than the weight listed on the label? The owner of the compa nv considers two proposals to reduce the proportion of bags w hose weight is less than the weight listed on the label. The rst proposition is to make change the average weight to 6.5 kg and leave the standard deviation as is. The second proposition is to keep the avelage weight at 5.4 kg and decrease the standard deviation from I13 kg to 0.2 kg. at What would be the proportion of bags that weigh less than the weight listed on the label if the owner opts for the rst proposal? b] What would be the proportion of bags that weigh less than the weight listed on the label ifthe owner opts for the second proposition? c] What proposal would I,rou recommend to the owner? At what average should the owner set the machine if he wants onlv 1MB of bags weigh less than the label weight? An inspector from a government agencyI visits the factorv to ensure product labeling regulations are followed. He tak ten bags at random among those which have just been lled bv the machine and he weighs the contents. of each of the bags using a verI..II precise scale. One of the bags onlwI needs to weigh less than 5 kg to that it issue a nding of non-compliance. If the machine is set so that the average quantityI [.1 poured in is alwavs equal at 6.4 kg and the standard deviation o = 0.3 kg, what is the probabilitv that the inspector will issue a notice of non-com pliance