Question

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.

Answer 1

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.