Evaluate Using the Given Value z=(x-mu)/sigma , mu

$z = \frac{x - μ}{σ}$ , $μ$

Step 1

Rewrite the equation as $\frac{x - μ}{σ} = z$ .

$\frac{x - μ}{σ} = z$

Step 2

Multiply both sides by $σ$ .

$\frac{x - μ}{σ} σ = z σ$

Step 3

Simplify the left side.

Cancel the common factor of $σ$ .

Cancel the common factor.

$\frac{x - μ}{σ} σ = z σ$

Rewrite the expression.

$x - μ = z σ$

Step 4

Solve for $μ$ .

Subtract $x$ from both sides of the equation.

$- μ = z σ - x$

Divide each term in $- μ = z σ - x$ by $- 1$ and simplify.

Divide each term in $- μ = z σ - x$ by $- 1$ .

$\frac{- μ}{- 1} = \frac{z σ}{- 1} + \frac{- x}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{μ}{1} = \frac{z σ}{- 1} + \frac{- x}{- 1}$

Divide $μ$ by $1$ .

$μ = \frac{z σ}{- 1} + \frac{- x}{- 1}$

Simplify the right side.

Simplify each term.

Move the negative one from the denominator of $\frac{z σ}{- 1}$ .

$μ = - 1 \cdot (z σ) + \frac{- x}{- 1}$

Rewrite $- 1 \cdot (z σ)$ as $- (z σ)$ .

$μ = - (z σ) + \frac{- x}{- 1}$

Dividing two negative values results in a positive value.

$μ = - z σ + \frac{x}{1}$

Divide $x$ by $1$ .

$μ = - z σ + x$