Question

2. Suppose that all possible n = 50 samples are selected from a population. How would the mean,

Answer 1

Using the Central Limit Theorem, it is found that the mean and the shape would remain the same, while the standard deviation would be multiplied by the square root of 2.

Central Limit Theorem

The Central Limit Theorem establishes 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 skewed variable, the sampling distribution is also approximately normal, as long as n is at least 30.

In this problem:

• The sample size would remain above 30, hence the shape would still be normal.

• The mean does not depend on the sample size, hence it would remain constant.

• The standard deviation is inversely proportional to the square root of the sample size, then since the sample size would be divided by 2, the standard deviation would be multiplied by the square root of 2.

More can be learned about the Central Limit Theorem at brainly.com/question/24663213