A bottling company uses a filling machine to fill glass bottles with mango juice. The bottles are supposed to contain 300 milliliters (ml). In fact the amounts vary according to a normal distribution with mean = 298 and standard dev = 3 ml. What is the probability that an individual bottle contains less than 295 ml?
This was addressed in a later post.
To find the probability that an individual bottle contains less than 295 ml, we can use the normal distribution and the given mean and standard deviation.
First, let's standardize the value of 295 ml using the formula for standardization:
z = (x - μ) / σ
where z is the z-score, x is the value we want to find the probability for, μ is the mean, and σ is the standard deviation.
Plugging in the values, we have:
z = (295 - 298) / 3 = -1
Next, we need to find the cumulative probability for this z-score. You can use a standard normal distribution table or a statistical calculator to find the corresponding probability.
Using a standard normal distribution table, the cumulative probability for a z-score of -1 is approximately 0.1587.
Therefore, the probability that an individual bottle contains less than 295 ml is approximately 0.1587 or 15.87%.
Note that this calculation assumes a normal distribution of the filling machine's output and that the variation follows a normal distribution.