precision???

Question

a soft drink sales person claims that the company puts exactly 355 mL of pop inot each can. Is this possible? If you were asked to describe the precision of this volume, how woudl you explain it?

Answer 1

It i svery likely to be within 1% accurate since the machines that do the work are tightly controlled to keep the consumer happy and to manage cost. I know that the tolerances of the can itself are within .2% based on a project I did using the cans.

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Answer 2

The answer to the question hinges on the word "Exactly".

There would be variation in every can but if this variation was kept sufficiently small say plus or minus .005 ml. Then the salesman could claim "exact" and have scientific support for the 355 mL. The variation is so small it is beyond the realm of significant digits. Each can could have 354.995 to 355.005 mL which could be argued as being exactly 355 mL. This is close enough to being exact in the scientific community.

Answer 3

What a mathematician means by "exactly" and what is meant by "exactly" in ordinary usage are not the same thing.

In reality there is no such thing as a mathematically exact physical measurement. All measurements we can make have to be reduced to a number with a finite number of digits, which is an ultimate limit on accuracy. That's apart from errors in the machine - many, many physical measurements are reported with more numerical precision than the machine really justifies.

What the sales person meant was something like, "the errors in the machine are so small that you won't likely care about them," or perhaps, "the errors in my machine are substantially smaller than in my competitor's."

Answer 4

The pump that pumps the liquid into the can has a chamber that fills up with exactly 355 mL of pop before then squirting it all in a can.

Answer 5

They would have to sample a number of containers, measure the amount and measure the mean, the standard deviation, 3* the standard deviation, the max and the min values of those samples. If the mean + or - the standard deviation falls within the max or min, that means good control. If the mean + or - 3* the standard deviation fall inside the max or min values, they have a high degree of confidence in their precision.