Answer:
The mean is 40.35 and the standard deviation is 0.13.
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].
For a certain type of olivine assembly, the silicon dioxide (SiO2) content (in weight percent) in a randomly chosen rock has mean 40.35 and standard deviation 0.4.
Sample of 10:
By the Central Limit Theorem, the mean is 40.35, and the standard deviation is [tex]s = \frac{\sigma}{\sqrt{n}} = \frac{0.4}{\sqrt{10}} = 0.13[/tex]
The mean is 40.35 and the standard deviation is 0.13.
