9 points) In a normally distributed data set, find the value of the standard deviation if the following information is given.
a. The mean is 226.2. x = 230. z = 0.2. Standard deviation
0.2 = (230-226.2)/SD
0.2SD = 3.8
SD = 19
To find the value of the standard deviation in a normally distributed dataset, we need to use the Z-score formula:
Z = (x - μ) / σ
Where:
Z = Z-score
x = Data point
μ = Mean
σ = Standard deviation
In this case, we are given:
Mean (μ) = 226.2,
Data point (x) = 230, and
Z-score (Z) = 0.2.
We can rearrange the formula to solve for the standard deviation (σ):
σ = (x - μ) / Z
Plugging in the given values:
σ = (230 - 226.2) / 0.2
Calculating this expression:
σ = 3.8 / 0.2
σ = 19
Therefore, the value of the standard deviation in this normally distributed dataset is 19.