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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?

Think about the idea behind sampling and that of the importance of standard error.

Use z-scores and the z-score formula.

Formula: z = (x - mean)/sd -->sd = standard deviation

Your values to plug into the formula are:
x = 295
mean = 298
sd = 3

Once you determine the z-score, check a z-table (normal distribution table) for the probability. Remember that the question is asking "less than 295 ml" so you will need to take that into consideration when looking at the table.

It helps to know how to read tables to do these kinds of problems.

For part 2, you will need to take the sample size into consideration by using this formula: z = (x - mean)/(sd/√n)
...then determine your probability using the table again.

I hope this will help get you started.

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