I need help with the following question. I do not know how to solve it.

IQ scores are normally distributed with a mean of 95 and a standard deviation of 18. Assume that many samples of size n are taken from a large population of people, and the mean IQ score is computed for each sample.

a. if the sample size is n=64, find the mean and standard deviation of the distribution of sample means

The solution was provided below:

Explanation:

Step 1:

Solution:

Given that,

mean = = 95

standard deviation = = 18

n = 64

Step 2:

= 95

• = / n = 18/ 64 = 2.25

Now, I need to determine the following:

Why is the standard deviation in part a different from the standard deviation in part b? I have been given the answers below:

1. With smaller sample sizes(as in parta), the means tend to be closertogether, so they have lessvariation, which results in a smaller standard deviation.
2. With smaller sample sizes(as in parta), the means tend to be furtherapart, so they have morevariation, which results in a smaller standard deviation.
3. With larger sample sizes(as in partb), the means tend to be furtherapart, so they have morevariation, which results in a bigger standard deviation.
4. With larger sample sizes(as in partb), the means tend to be closertogether, so they have lessvariation, which results in a smaller standard deviation.

Which one is the correct answer?