12)

University researchers examined the process of lling plastic pouches of dry blended biscuit mix. The current ll mean of the process is set at p: 406 grams, and the process ll standard deviation is 6 = 10.3 grams. Operators monitor the process by randomly sampling 38 pouches each day and measuring the amount of biscuit mix in each. Consider i, the mean ll amount of the sample of 38 products. Suppose that on one particular day, the operators observe i= 400.7. One of the operators believes that this indicates that the true process ll mean u for that day is less than 406 grams. Another operator argues that p =406, and the small value of )1 observed is due to random variation in the ll process. Which operator do you agree with? Why? The operator that believes that the mean is V should be believed because the probability that the sample mean would be 400.? or less if the true mean was 406 is . (Round to three decimal places as needed.)