The label attached to the "XXL 90% cocoa" bars from the Rose Noire chocolate shop indicates 500 g. If the bars under this label were lighter, Rose Noire would risk having to pay a hefty fine as it would violate the standards dictated by federal food labeling law. At the chocolate shop, the quantity poured by the machine into each bar mold follows a normal distribution with a standard deviation of 5 g. The mean poured into each mold by the machine depends on the chosen control parameter. To ensure that the bars contain at least 500 g, it is set at 510 g (the mold can contain up to 530 g). a) [1 point] Based on these parameters, estimate the proportion of bars that exceed 500 g. Round to four decimal places. b) [2 points] To verify that the process is under control, 5 bars are sampled per hour at each hour of production. What should be the lower and upper control limits for "Z=3"? Round to one decimal place. c) [1 point] It is now realized that pouring 510 g into each mold to comply with the law results in costly waste. After discussions, it has been decided to reduce the filling parameter from 510 g to 506 g, while still respecting the proportion calculated in part a). This will require a new machine that must be much more precise. In particular, what should be the standard deviation of this new machine