Respuesta :
Answer:
The standard deviation of the distribution of sample means for samples of size 60 is of 1.2264.
Step-by-step explanation:
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].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
Standard deviation is 9.5 for a population.
This means that [tex]\sigma = 9.5[/tex]
Sample of 60:
This means that [tex]n = 60[/tex]
What is the standard deviation of the distribution of sample means for samples of size 60?
[tex]s = \frac{\sigma}{\sqrt{n}} = \frac{9.5}{\sqrt{60}} = 1.2264[/tex]
The standard deviation of the distribution of sample means for samples of size 60 is of 1.2264.
