Answer:
The mean of the sampling distribution is 20 and the standard deviation is 2.89.
Step-by-step explanation:
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of 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].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
Population:
Mean 20, standard deviation of 5.
Sampling distribution:
3 rounds
Mean = 20
[tex]s = \frac{5}{\sqrt{3}} = 2.89[/tex]
The mean of the sampling distribution is 20 and the standard deviation is 2.89.
