Respuesta :
Using the Central Limit Theorem, it is found that the distribution of the sample mean of six randomly selected bottles is approximately normal, with mean 473 ml and standard error of 1.22 ml.
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
In this problem, for the population, we have that:
[tex]\mu = 473, \sigma = 3[/tex]
Then, for the sample of n = 6:
[tex]s = \frac{3}{\sqrt{6}} = 1.22[/tex]
More can be learned about the Central Limit Theorem at https://brainly.com/question/24663213
