SOLUTION: "Bottling an energy drink". A bottling company uses a filling machine to fill cans with an energy drink. The cans are supposed to contain 250 milliliters (ml) each. The machine, ho

Question 1191499: "Bottling an energy drink". A bottling company uses a filling machine to fill cans with an energy drink. The cans are supposed to contain 250 milliliters (ml) each. The machine, however, has some variability, so the standard deviation of the volume is σ=0.27. A sample of five cans is inspected each hour for process control purposes, and records are kept of the sample mean volume. If the process mean is exactly equal to the target value, what are the mean and standard deviation of the numbers recorded?

Answer by CPhill(1987) (Show Source): You can put this solution on YOUR website!
Here's how to determine the mean and standard deviation of the recorded sample means:
* **Mean:** The mean of the sample means will be equal to the population mean (the target value). In this case, the mean is 250 ml.
* **Standard Deviation:** The standard deviation of the sample means is called the standard error. It's calculated by dividing the population standard deviation by the square root of the sample size.
Standard Error = σ / √n
Where:
* σ is the population standard deviation (0.27 ml)
* n is the sample size (5 cans)
Standard Error = 0.27 / √5 ≈ 0.1207 ml
So, the mean of the recorded numbers (sample means) will be 250 ml, and the standard deviation will be approximately 0.1207 ml.

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