Answer:
The sampling distribution has a mean of $1,500 and a standard deviation of $47.67
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 of at least 30 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 = 500, n = 110[/tex]
So
[tex]s = \frac{500}{\sqrt{110}} = 47.67[/tex]
The sampling distribution has a mean of $1,500 and a standard deviation of $47.67
