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.
<em />
<em>Let </em><em> = sample mean volume of liquid in bottles</em>
The Sampling distribution of the sample mean also follows normal distribution;
As we know that ; Population mean = = 500 ml
Population Standard deviation = = 2 ml
n = sample of bottles = 20
<u>Now, the mean of sampling distribution is given by;</u>
Sample Mean, = Population mean = 500 ml
<u>And, standard deviation of the sampling distribution of this sample mean is given by;</u>
Standard deviation = = = 0.447 ml
Hence, the standard deviation of the sampling distribution of this sample mean is 0.447 ml.