Fertilizer is sold in bags. The standard deviation of the content of a bag is 0.43 kg. Weights of fertilizer in bags are normally distributed. 40 bags are piled on a pallet and weighed.
a) If the net weight of fertilizer in the 40 bags is 826 kg, (i) what percentage of the bags are expected to contain less than 20.00 kg each? (ii) find the 10th percentile (or smallest decile) of weight of fertilizer in a bag.
b) How many pallets, carrying 40 bags each, will have to be weighed so that there is at least 96% probability that the true mean weight of fertilizer in a bag is known within 0.05 kg?