Aquality control officer is randomly checking the weights of pumpkin seed bags being filled by an automatic filling machine. each bag is advertised as weighing 400 grams. a bag must weigh within 2.1 grams in order to be accepted. what is the range of rejected bags, x, for the bags of pumpkin seeds?

An automated water dispenser fills packets with one liter of water on average, with a standard deviation of 5 milliliter. the manual says that after a year of operation the dispenser should be tested to see if it needs recalibration. a year later a number of filled packets are set aside and measured separately. it is found that the average packet now contains about 0.995 liters. does the dispenser need calibration? explain your answer.