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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?

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JeanaShupp

Answer: 0.3085

Step-by-step explanation:

Given: Mean : [tex]\mu=300\text{ ml}[/tex]

Standard deviation : [tex]\sigma=10\text{ ml}[/tex]

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

[tex]z=\dfrac{X-\mu}{\sigma}[/tex]

For X = 295 ml, we have

[tex]z=\dfrac{295-300}{10}=-0.5[/tex]

The p-value of z = [tex]P(Z=z<-0.5)=0.3085[/tex]

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

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