Answer:
When the sample size is increased from n = 9 to n = 45, the standard deviation of the sample mean decreases from 1.167 to 0.522.
Step-by-step explanation:
The Central Limit Theorem estabilishes that, for a random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], 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, we have that:
[tex]\sigma = 3.5[/tex]
n = 9
[tex]s = \frac{3.5}{\sqrt{9}} = 1.167[/tex]
n = 45
[tex]s = \frac{3.5}{\sqrt{45}} = 0.522[/tex]
When the sample size is increased from n = 9 to n = 45, the standard deviation of the sample mean decreases from 1.167 to 0.522.
