Answer:
n = 6: [tex]s = 1.4289[/tex]
n = 49: [tex]s = 0.5[/tex]
As the sample size is increased, standard deviation of the sample mean decreases.
Step-by-step explanation:
The standard deviation of the sample mean is the standard deviation off the population[tex]\sigma[/tex] divided by the square root of the size of the sample, that is [tex]n[/tex]. Mathematically, that is
[tex]s = \frac{\sigma}{\sqrt{n}}[/tex]
In this problem, we have that:
A synthetic fiber used in manufacturing carpet has tensile strength that is normally distributed with a standard deviation of 3.5 psi. So [tex]\sigma = 3.5[/tex]
So:
n = 6
[tex]s = \frac{3.5}{\sqrt{6}} = 1.4289[/tex]
n = 49
[tex]s = \frac{3.5}{\sqrt{49}} = 0.5[/tex]
As the sample size is increased, standard deviation of the sample mean decreases.
