# Central limit theorem/sampling distribution of a sample mean

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

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?

https://brainmass.com/statistics/central-limit-theorem/central-limit-theorem-sampling-distribution-of-a-sample-mean-5759

#### Solution Summary

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

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?