Sagot :
Answer:
By the Central Limit Theorem, the mean is 78, the standard deviation is [tex]s = \frac{6}{\sqrt{n}}[/tex] and the shape is approximately normal.
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.
Mean of 78 and a standard deviation of 6
This means that [tex]\mu = 78, \sigma = 6[/tex]
Samples of n:
This means that the standard deviation is:
[tex]s = \frac{\sigma}{\sqrt{n}} = \frac{6}{\sqrt{n}}[/tex]
What are the mean, standard deviation, and shape of the distribution of x-bar for n?
By the Central Limit Theorem, the mean is 78, the standard deviation is [tex]s = \frac{6}{\sqrt{n}}[/tex] and the shape is approximately normal.