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 1,008g with standard deviation of 6g. Complete parts (a) and (b) below.

Part 1

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