the mean of a normally distributed set of data is 21.1. a data value of 13.7 has a z-score of -2.40. determine the standard deviation of this distribution
We can use the formula for z-score to find the standard deviation:
z = (x - μ) / σ
where z is the z-score, x is the data value, μ is the mean, and σ is the standard deviation.
Plugging in the values we know, we get:
-2.40 = (13.7 - 21.1) / σ
Multiplying both sides by σ:
-2.40σ = 13.7 - 21.1
Simplifying:
-2.40σ = -7.4
Dividing both sides by -2.40:
σ = 3.083...
Rounding to two decimal places, the standard deviation is approximately 3.08.