Cereal Manufacturer The plant manager of a cereal manufacturer is wondering if the company could save some cereal by slightly lowering the cereal content of each box. Studying a major product, a 454 gram (net weight) ready-to-eat cereal, the manager discovers that four boxes are routinely taken from the filling machine every 10 minutes and weighed. Data for approximately 2.5 hours of inspection are shown below. Questions 1. Is the process in control? 2. Determine what weight the filler head is likely set to. 3. If the Weights and Measures Act dictates that the tolerance for weight of a product of approximately 454 grams is 2 grams, what is the probability that an inspector will find a legally defined underweight box (i.e., weighing less than 452 grams)? 4. Has the filler head been set too conservatively? Discuss. Samples 1 2 10 11 12 13 14 15 455.5 456.0 456.0 452.5 456.0 452.0 457.5 454.5 456.0 453.0 455.0 458.0 457.5 458.0 460.0 460.0 455.5 453.0 455.0 456.0 455.0 455.5 453.0 454.0 455.0 457.5 456.0 456.5 453.0 455.5 456.5 456.0 454.0 453.0 455.0 453.0 457.0 453.0 453.0 456.0 456.5 454.5 453.0 456.5 454.5 456.5 456.0 455.0 455.0 454.5 456.0 452.0 458.0 455.0 456.5 456.5 454.0 455.5 456.0 457.0