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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