Question

A bottling company uses a filling machine to fill plastic bottles with popular cola. The contents are known to vary according to a normal distribution with mean μ = 300 ml and standard deviation σ = 10 ml. What is the probability that the mean contents of the bottles in a six pack is less than 295 ml?

Answer 1

Answer: 0.3085

Step-by-step explanation:

Given: Mean : $\mu=300\text{ ml}$

Standard deviation : $\sigma=10\text{ ml}$

The formula to calculate the value of z-score :-

$z=\dfrac{X-\mu}{\sigma}$

For X = 295 ml, we have

$z=\dfrac{295-300}{10}=-0.5$

The p-value of z = $P(Z=z<-0.5)=0.3085$

Hence, the probability that the mean contents of the bottles in a six pack is less than 295 ml =0.3085