Respuesta :
Answer:
a) 2.66
b) 9
Step-by-step explanation:
Central Limit Theorem
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].
part A: what is the standard deviation of the sampling distribution of x hat? show your work.
We have that [tex]\sigma = 8.4, n = 10[/tex]. So
[tex]s = \frac{\sigma}{\sqrt{n}} = \frac{8.4}{\sqrt{10}} = 2.66[/tex]
PartB: what does the sample size need to be if you want the standard deviation of the sampling distribution of x hat to be 2.8?
This is n when [tex]s = 2.8[/tex]. So
[tex]s = \frac{\sigma}{\sqrt{n}}[/tex]
[tex]2.8 = \frac{8.4}{\sqrt{n}}[/tex]
[tex]2.8\sqrt{n} = 8.4[/tex]
[tex]\sqrt{n} = \frac{8.4}{2.8}[/tex]
[tex]\sqrt{n} = 3[/tex]
[tex](\sqrt{n})^2 = 3^2[/tex]
[tex]n = 9[/tex]
