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A bottling company uses a filling machine to fill glass bottles with mango juice. The bottles are supposed to contain 300 milliliters (ml). In fact the amounts vary according to a normal distribution with mean = 298 and standard dev = 3 ml. What is the probability that an individual bottle contains less than 295 ml?

Part 2 - What is the probability that the average content of a 4 pack of bottles is less than 295 ml?

With one bottle, you can use the Z-score.

Z = (X - mean)/SD = (295 - 298)/3 = -3/3 = -1

If you have memorized the major divisions of the areas in a normal distribution as indicated by the standard deviation (SD), you would know that 16% of the scores lie below this point = .16.

If you don't know these proportions, consult a table in the back of your statistics text called something like "areas under the normal distribution."

For the 4 bottles, you use the same formula. However, this time — since you are dealing with a sample mean rather than just an individual score — instead of dividing by the SD, you divide by the standard error of the mean (SE).

Z = (X - mean)/SE, where

SE = SD/sq.rt. of N

Solve for Z and look it up in that table to get your answer.

I hope this helps. Thanks for asking.

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