The mean of a normally distributed data set is 226.2. The data item, 230, has a z-score of 0.2. Find the standard deviation.
Z = (score-mean)/SD
Insert the values and calculate.
yguyg
To find the standard deviation, we need to use the formula for z-score.
The formula for z-score is:
z = (x - μ) / σ
Where:
z is the z-score
x is the data item
μ is the mean
σ is the standard deviation
Using the given information, we can rearrange the formula to solve for the standard deviation:
σ = (x - μ) / z
Plugging in the values:
x = 230
μ = 226.2
z = 0.2
We can substitute these values into the formula:
σ = (230 - 226.2) / 0.2
Calculating the expression on the right side:
σ = 3.8 / 0.2
Simplifying the expression:
σ = 19
Therefore, the standard deviation is 19.