A bottle filling system puts your probability calculus to the test

It is very important to drink more on hot days. This is why we dedicate this Q-QUIZ to a bottle filling system and associated beverages and test your knowledge in probability calculation.

1) The filling volume of a bottle filling system is normally distributed with an average of 1000 ml and a variation of 1 ml. What is the probability of blind-drawing a bottle whose filling volume is between 1001 and 1002 ml?

  • About 13.6%
  • About 84.1%
  • Between 13.6% and 97.7%


2) The normal probability plot shows filling volumes of a different filling process. Two points are very significant:
1st point: filling volume of 1001 ml / probability of 50 %
2nd point: filling volume of 1002 ml / probability of 84.1345 %
What is the standard deviation of the filling volume of this system?

  • 2
  • 0.5
  • 1


3) You took a sample before and after maintaining a filling system. The chart of the values collected after the maintenance is significantly steeper than the chart of the first sample. This fact usually indicates that the maintenance…

  • … reduced the variation (standard deviation).
  • … reduced the process level (average).
  • … reduced the variation and the process level.


4) Data of several subgroups were combined into a single data set and plotted in a normal probability plot. The corresponding chart is s-shaped. This shape shows that…

  • … the variation improved.
  • … data from different populations were combined.
  • … there are too many outliers.


5) The values of a sample (size > 100) represent the filling volumes of lemonade. A normal probability plot shows them. The data a clearly skewed to the right which indicates that…

  • … the data come from a normally distributed population.
  • … there are too few data available to render a judgement.
  • … the data come from a not normally distributed population.


6) The beverage company offers a special edition of bottles. 50% of all these bottles have a win code in the bottle cap. What is the probability of having a single win code when you select two bottles?

  • 0.25
  • 0.5
  • 0.75


7) While printing bottle labels, there are normally two misprints on each 100 running meters. What is the probability that a sample of 10 running meters shows exactly 1 misprint?

  • 0.164%
  • 1.64%
  • 16.4%


8) You bought eleven small bottles of apple juice, five small bottles of orange juice and four little bottles of cherry juice for a picnic and put them in a bag. What is the probability of blind-drawing a bottle of orange juice from the bag?

  • 25%
  • 20%
  • 22.5%


Our Q-QUIZ is published once a month. You can find the answer to all questions of the current quiz online with the release of the next quiz.