A machine that fills bottles with a beverage has a fill volume whose mean is 25.01 ounces, with a standard deviation of 0.02 ounces. a case consists of 24 bottles randomly sampled from the output of the machine. find the standard deviation of the total volume of the beverage in the case.

The standard deviation in the case is 0.004.

The population mean is 25.01 and the population standard deviation is 0.002. To find the sample standard deviation, we use

σₓ = σ / (√n), where σ is the population standard deviation and n is the sample size. Using our information we have:

σₓ = 0.02 / (√24) =.004.