Respuesta :
Using the Central Limit Theorem, considering a normally distributed population with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution is normal, with mean [tex]\mu[/tex] and standard deviation [tex]0.5\sigma[/tex].
Central Limit Theorem
The Central Limit Theorem establishes 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].
Hence, considering a normally distributed population with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], and with the sample size of n = 4, the mean remains the same while the standard deviation is given by:
[tex]s = \frac{\sigma}{\sqrt{4}} = 0.5\sigma[/tex]
More can be learned about the Central Limit Theorem at https://brainly.com/question/24663213
