For a population that has a standard deviation of 10, figure the standard deviation of the distribution of means for samples of size 3.
To find the standard deviation of the distribution of means for samples of size 3, you need to use the formula for the standard error of the mean. The standard error of the mean (SEM) is the standard deviation of the sample means.
The formula for calculating the SEM is:
SEM = σ / √n
Where:
σ is the standard deviation of the population
n is the sample size
In this case, the standard deviation of the population is given as 10, and the sample size is 3.
Applying the values to the formula, we have:
SEM = 10 / √3
To calculate the exact value, divide 10 by the square root of 3:
SEM ≈ 5.77
Therefore, the standard deviation of the distribution of means for samples of size 3 is approximately 5.77.