Question

A local brewery sells their beer in 330 ml bottles. On average the beer is filled with 328.3 ml with a standard deviation of 0.8 ml. Since it is possible to under-fill the bottle but impossible to fill the bottle with more than 330 ml, the distribution is:

a. Normal
b. Skewed Left
c. Skewed Right
d. Symmetrical

Answer 1

The local brewery's beer bottle filling distribution would be skewed left because there's a limit on overfilling but not on underfilling, leading to a longer tail on the left side.

Step-by-step explanation:

The distribution of beer in the bottles described would be skewed left. This is because it's possible to under-fill a bottle but not to overfill it past the 330 ml mark, placing a natural limit on the maximum value. Therefore, more bottles will be clustered just below the maximum limit, and fewer will be further away to the left. This causes a long tail to the left. If the distribution were symmetrical, there would be as many instances of overfilling as underfilling, but since the overfilling is capped at 330 ml, the distribution will be skewed left.

A normal distribution would not be applicable here due to the described constraints on the bottle filling. Normally, bell-shaped distributions are symmetric, mean that the mean, median, and mode are all in the same place. However, the constraint imposed by the maximum fill level disrupts this symmetry, resulting in a skewed distribution.