Intravenous fluid bags are filled by an automated filling machine. Assume that the fill volumes of the bags are independent, normal random variables with a standard deviation of 0.08 fluid ounces. (a) What is the standard deviation of the average fill volume of 24 bags? Round your answer to four decimal places.

Let X the random variable that represent the heights of a population, and for this case we know the distribution for X is given by:

Where and

Since the distribution for X is normal then the  we know that the distribution for the sample mean is given by:

And the standard error is given by:

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".  

Solution to the problem

Let X the random variable that represent the heights of a population, and for this case we know the distribution for X is given by:

Where and

Since the distribution for X is normal then the  we know that the distribution for the sample mean is given by:

And the standard error is given by: