We operate a bottle filling factory. One of our machines fills a32-ounce bottle with a target of 32.08 ounces of orange juice.Every 10 minutes or so we obtain a sample filled bottle and hold itfor the quality control department who will weigh the approximately50 such bottles to determine if the machine is performingcorrectly. If the average of the 50 bottles is less than 32 ounces,the machine is shut down and the entire production from that 8-hourshift is held until further tests are performed.
- We know that over the years this machine delivers 32.082 ounceof orange juice with a standard deviation 0.01 ounces. What is theprobability that a sample of 50 bottles has a mean volume of lessthan 32 ounces?
- There are 1,008 8-hour shifts per year (allowing for holidays,maintenance and a two-week scheduled shutdown). In a typical year,hour many times do we expect the quality department to shut downthe machine and hold that shift’s production?
