For a population that has a standard deviation of 10, figure the standard deviation of the distribution of means for samples of size 3.
Take the standard deviation and divide it by the square root of the sample size.
To calculate the standard deviation of the distribution of means for samples of size 3, you need to use the concept of the standard error of the mean (SEM).
The formula to calculate the SEM is:
SEM = σ / √n
Where:
- SEM is the standard error of the mean
- σ is the population standard deviation
- n is the sample size
In this case, the population standard deviation (σ) is given as 10, and the sample size (n) is 3. Plugging these values into the formula, we get:
SEM = 10 / √3
Now, we can calculate the standard deviation of the distribution of means by multiplying the SEM by the square root of the sample size:
Standard Deviation of the Distribution of Means = SEM * √n
Standard Deviation of the Distribution of Means = (10 / √3) * √3
Simplifying this expression, we find:
Standard Deviation of the Distribution of Means = 10
Therefore, the standard deviation of the distribution of means for samples of size 3 in this particular population with a standard deviation of 10 would also be 10.