Question

An article describes the chemical compositions of certain minerals in the early Archaean mantle. 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. Find the mean and standard deviation of the sample mean SiO2 content in a random sample of 10 rocks. Round the mean to two decimal places. Mean Standard deviation

Answer 1

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 $\mu$ and standard deviation $\sigma$, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$.

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 $s = \frac{\sigma}{\sqrt{n}} = \frac{0.4}{\sqrt{10}} = 0.13$

The mean is 40.35 and the standard deviation is 0.13.