Solve each formula for the specified variable. Assume that the denominator is not 0 if variables appear in the denominator. z = x-μ/σ, for x (standardized value)

Verified step by step guidance

1. Start with the given formula: $z = \frac{x - \mu}{\sigma}$.
2. To isolate $x$, first multiply both sides of the equation by $\sigma$ to eliminate the denominator: $z \cdot \sigma = x - \mu$.
3. Next, add $\mu$ to both sides of the equation to solve for $x$: $x = z \cdot \sigma + \mu$.

Key Concepts

Algebraic Manipulation

Algebraic manipulation involves rearranging equations to isolate a specific variable. This process includes operations such as adding, subtracting, multiplying, or dividing both sides of the equation by the same value. Understanding how to manipulate equations is essential for solving for a variable, especially in formulas where variables are interdependent.

Standardization in Statistics

Standardization is a statistical technique used to convert a variable into a standardized score, known as a z-score. The formula z = (x - μ) / σ represents how many standard deviations an element is from the mean (μ) of a distribution, with σ being the standard deviation. This concept is crucial for interpreting data in a standardized format, allowing for comparison across different datasets.

Denominator Restrictions

In algebra, it is important to recognize that certain expressions cannot have a denominator equal to zero, as this would make the expression undefined. When solving equations, one must ensure that any variable in the denominator does not take on values that would lead to division by zero. This understanding is vital for maintaining the validity of the solutions derived from the equations.