For a population that has a standard deviation of 10, figure the standard deviation of the distribution of means for samples of size- (b) 3.
To calculate the standard deviation of the distribution of means for samples of size 3, we need to use the formula for the standard deviation of a sample mean:
Standard Deviation of the Distribution of Means = Standard Deviation of the Population / Square Root of Sample Size
In this case, the standard deviation of the population is given as 10, and the sample size is 3.
So, plugging in the values into the formula:
Standard Deviation of the Distribution of Means = 10 / √3
To simplify this, we need to find the square root of the sample size (√3).
The square root of 3 is approximately 1.732.
Now, substitute the value back into the formula:
Standard Deviation of the Distribution of Means ≈ 10 / 1.732
Using a calculator, the result is approximately 5.774.
Therefore, the standard deviation of the distribution of means for samples of size 3 is approximately 5.774.