Question

A process that fills plastic bottles with a beverage has a mean fill volume of 2.013 L and a standard deviation of 0.005 L. A case contains 18 bottles. Assuming that the bottles in a case are a simple random sample of bottles filled by this method, find the mean and standard deviation of the average volume per bottle in a case. studysoup

Answer 1

Explanation:

Given that

X1, X2, X3....... X18 are the volume of beverages in 18 bottles. These volumes have the same distribution and are independent of each other.

E.X(i) = 2.013L, while the Standard Deviation is given as

S D = X(i) = 0.005L

The average volume per bottle = X bar

E.X bar = E.X(i) = 2.013L

S D X bar = [S D X(i)]/√n = 0.005 /√18 = 0.005 / 4.24 = 1.18*10^-3L