A bottler carefully weighs bottles coming off its production line to check that the system is filling the bottles with the correct amount of beverage. By design, the system is set to slightly overfill...

A bottler carefully weighs bottles coming off its production line to check that the system is filling the bottles with the correct amount of beverage. By design, the system is set to slightly overfill the bottles to allow for random variation in the packaging. The content weight is designed to be 1,020 g with standard deviation 8 g. Assume that the weights are normally distributed. (Use tables or software for the normal distribution.)

(a) A proposed system shuts down the facility if the contents of a bottle weigh less than 1,000 g. What is the chance of a Type I error with this system?

(b) Suppose the mean content level of bottles were to fall to 1,000 g. What is the chance that the proposed system will miss the drop in average level and commit a Type II error?