Weights of erasers produced by a certain factory are known to follow the uniform distribution between 31.5 g and 32.3 g.

(a) (10 points) erasers produced by this factory are sold in packs of 45. a retailer randomly bought 200 packs. find the probability that, for at least 15 packs, the average weight of the erasers in the pack is at least 31.95 g.

(b) (10 points) each day, a quality control unit examines the erasers produced by this factory.the unit randomly chooses an eraser from the outputs of this factory and weighs it. this process is repeated 50 times. the unit then records the total number of erasers that were found to weigh at least 31.7 g. (erasers with weights at least 31.7 g are called "good" erasers)suppose this unit works for 42 consecutive days. find the probability that, on average, it finds at least 37.2 "good" erasers per day