Question

A bottling company uses a filling machine to fill plastic bottles with cola. The bottles are supposed to contain 300 milliliters (ml). In fact, the contents vary according to a Normal distribution with mean = 298 ml and standard deviation = 3 ml.What is the probability that the contents of a randomly selected bottle is less than 295 ml?0.15870.99280.84130.00720.0478

Answer 1

Solution:

Given:

$\begin{gathered} \mu=298ml \\ \sigma=3ml \\ x=295ml \end{gathered}$

To get the probability, we first need to calculate the Z-score for the data given using the Z-score formula below;

$Z=\frac{x-\mu}{\sigma}$

Substituting the given values into the formula;

$\begin{gathered} Z=\frac{295-298}{3} \\ Z=\frac{-3}{3} \\ Z=-1 \end{gathered}$

From Z-score tables,

The probability that the content of the selected bottle is less than 295ml is;

[tex]\begin{gathered} P(x<295)=P(x

Therefore, the probability that the content of the selected bottle is less than 295ml is 0.1587