A bottling company uses a filling machine to fill plastic bottles with a popular cola. The bottles are supposed to contain 300 m
l. In fact, the contents vary according to a normal distribution with mean μ = 298 ml and standard deviation σ = 3ml. What is the probability that a randomly selected bottle contains less than 295 ml?
For a normal distribution, the 68-95-99.7 rule says that 68% of the distribution lies within 1 standard deviation from the mean, 95% within two standard deviations and 99.7% within three standard deviations.
From the question,
Mean μ = 298 ml
Standard deviation σ = 3 ml
A value of 295 ml is within one standard deviation = 68%.
Since it's on the lower side, it's within 68% ÷ 2 = 34%.
The lower half below the mean is 50% of the distribution. Hence, for a selection less than 1 standard deviation, the probability is
