The formula for a z-score is
We don't have μ, the mean, or σ, the standard deviation. We can, however, set up a system of two equations with the information we do have. We know:
We can make this look more like a "typical" system of equations by cancelling the fractional part of each equation. We do this by multiplying the bottom of each equation by σ:
Now we'll get the variables on the same side of the equation. We'll do this by adding μ to both sides:
Now we'll write this vertically:
We will "eliminate" μ by subtracting the bottom equation:
Divide both sides by -5:
Our standard deviation is 5. Substituting this into our top equation we have:
-3(5)+μ=60
-15+μ=60
Cancel the -15 by adding it to both sides:
-15+μ+15=60+15
μ=75
Our mean is 75.
We don't have μ, the mean, or σ, the standard deviation. We can, however, set up a system of two equations with the information we do have. We know:
We can make this look more like a "typical" system of equations by cancelling the fractional part of each equation. We do this by multiplying the bottom of each equation by σ:
Now we'll get the variables on the same side of the equation. We'll do this by adding μ to both sides:
Now we'll write this vertically:
We will "eliminate" μ by subtracting the bottom equation:
Divide both sides by -5:
Our standard deviation is 5. Substituting this into our top equation we have:
-3(5)+μ=60
-15+μ=60
Cancel the -15 by adding it to both sides:
-15+μ+15=60+15
μ=75
Our mean is 75.
