Answer to Question #308289 in Statistics and Probability for Flipper

Question

A bottling company uses a filling machine to fill plastic bottles with a popular cola. The bottle are supposed to contain 300 millilimeters. In fact, the contents vary according to a normal distribution with mean =298 ml and standard deviation = 3ml.

a. What is the probability that an individual bottle contains less than 295 ml?

b. What is the probability that the mean contents of the bottles in a six-pack is less than 295 ml?

Answer 1

we use z calculations

a) z(295) = (295 - 298)/ (3) = -1

Thus p(x<295) = p(z<-1)

using normal tables, we obtain that p(z<-1) = 0.15866 which is the required solution

b) we define the new standard deviation as =(old standard deviation) / (n^1/2)

which becomes = (3)/ (6^1/2) = 1.224744871

hence z(295) = (295-298)/ (1.224744871) = -2.449489743 which is approximately -2.45

Thus p(x<295) = p(z<-2.45) = 0.00714 which is the required solution.