Answer:
The approximate standard deviation of the sampling distribution of the mean for all samples with n = 40 is 2.8460.
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]
What is the approximate standard deviation of the sampling distribution of the mean for all samples with n = 40?
We have that [tex]\sigma = 18[/tex]
So
[tex]s = \frac{18}{\sqrt{40}} = 2.8460[/tex]
The approximate standard deviation of the sampling distribution of the mean for all samples with n = 40 is 2.8460.
