You have a box of 15 widgets whose average weight for each individual widget is 10 pounds with a standard deviation of 4.0 pounds. Based on this information, what is the standard deviation, taken to 4 decimal places, for the sample average of the weight of the widgets in the box?
To find the standard deviation of the sample average weight of the widgets, we need to use the formula:
Standard Deviation of Sample Mean (σ) = Standard Deviation of Population (σ) / √Sample Size (n)
First, we need to find the standard deviation of the population, which is given as 4.0 pounds.
Next, we need to find the sample size. In this case, the sample size is mentioned as 15 widgets.
Now, we can plug in these values into the formula:
σ = 4.0 pounds / √15
To calculate the value, divide the standard deviation of the population, 4.0 pounds, by the square root of the sample size, which is √15.
Using a calculator, the square root of 15 is approximately 3.87298.
Now, divide 4.0 pounds by 3.87298 to get the standard deviation of the sample mean:
σ ≈ 4.0 pounds / 3.87298 ≈ 1.0331 pounds
Rounded to four decimal places, the standard deviation, σ, for the sample average weight of the widgets is approximately 1.0331 pounds.