Respuesta :
Answer:
The standard deviation of the sampling distribution of the sample mean score for a random sample of 36 students is 1.
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.
In this problem, we have that:
[tex]\sigma = 6, n = 36[/tex]
Then, by the Central Limit Theorem:
[tex]s = \frac{\sigma}{\sqrt{n}}[/tex]
[tex]s = \frac{6}{\sqrt{36}}[/tex]
[tex]s = 1[/tex]
The standard deviation of the sampling distribution of the sample mean score for a random sample of 36 students is 1.
