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?
Accepted Solution
A:
Answer: 0.3085Step-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