Respuesta :
Answer:
The sampling distribution of the sample mean for samples of size 49 is approximately normally distributed with mean of 100 and standard deviation of 3.
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 100, standard deviation 21.
The sampling distribution of the sample mean for samples of size 49
By the Central Limit Theorem
Mean 100
Standard deviation
[tex]s = \frac{21}{\sqrt{49}} = 3[/tex]
The sampling distribution of the sample mean for samples of size 49 is approximately normally distributed with mean of 100 and standard deviation of 3.
