Question 1132735: Cans of regular soda have volumes with a mean of 12.63 oz and a standard deviation of 0.12 oz. Is it unusual for a can to contain 12.77 oz of soda?
Minimum "usual" value =____oz
Answer by Alex.33(110)   (Show Source):
You can put this solution on YOUR website! 12.77 is (12.77-12.63)/0.12=(7/6) standard deviations away from the mean.
I cannot be certain whether it is 'unusual', but by properties of the normal distribution, the possibility that the volume of a random can is within (7/6) STD is between 68.3%(within 1 STD from mean) and 95.4%(within 2 STD from the mean), closer to the former.
You can then decide whether this is 'unusual' based on the definition of 'usual'.
But to show how to solve the problem fully I now assume 'within 2 STD from the mean' to be 'usual'. If this is different than the definition you've given, the problem can be solved similarly.
Then the 12.77-oz soda is usual.
The minimum 'usual' value, under this definition, is 12.63-2*.12=12.39 oz.
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