Respuesta :
Answer:
The standard deviation of the sampling distribution of this sample mean is 0.447 ml.
Step-by-step explanation:
We are given that a bottling company fills bottles with a mean of 500 ml of liquia, with a standard deviation of 2 ml. Quality control randomly samples 20 bottles at a time.
Let [tex]\bar X[/tex] = sample mean volume of liquid in bottles
The Sampling distribution of the sample mean also follows normal distribution;
As we know that ; Population mean = [tex]\mu[/tex] = 500 ml
Population Standard deviation = [tex]\sigma[/tex] = 2 ml
n = sample of bottles = 20
Now, the mean of sampling distribution is given by;
Sample Mean, [tex]\bar X[/tex] = Population mean = 500 ml
And, standard deviation of the sampling distribution of this sample mean is given by;
Standard deviation = [tex]\frac{\sigma}{\sqrt{n} }[/tex] = [tex]\frac{2}{\sqrt{20} }[/tex] = 0.447 ml
Hence, the standard deviation of the sampling distribution of this sample mean is 0.447 ml.
