For 120 consecutive days, a process engineer has measured the temperature of champagne bottles as they are made ready for servin
g. Each day, she took a sample of 8 bottles. The average across all 960 bottles (120 days, 8 bottles per day) was 46 degrees Fahrenheit. The standard deviation across all bottles was 0.8 degrees Fahrenheit. what would be the center line
Center line can be said to be the X double bar. X double bar is the average value we have across all components we're considering. In this question, the X double bar is already given as 960 bottles (if you multiply 120 days by 8 bottles per day) and that it is 46 degrees Fahrenheit.
As such, there exist no reason to want to or have to solve for anything since it's already given.
Therefore the Centre line is 46 degrees Fahrenheit, same as what is given in the question.
The solution for this problem is:It's given that the heights are normally distributed. 5 feet 7 inches = (5*12 +7) inches = (60+7) inches = 67 inches. The z-score is (67 - 69.1)/(2.65) = -1.136. The probability is 0.127978 or 12.8%, making probability of a height over 67 inches
