(a) Solve $$ z=\frac{x-\mu}{\sigma} $$ for $$ \sigma $$

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UpStudy AI · Accepted Answer

To solve the equation $$ z = \frac{x - \mu}{\sigma} $$ for $$ \sigma $$, follow these algebraic steps:

1. **Start with the original equation:**
   $$
   z = \frac{x - \mu}{\sigma}
   $$

2. **Multiply both sides by $$ \sigma $$ to eliminate the denominator:**
   $$
   z \cdot \sigma = x - \mu
   $$
   
3. **Isolate $$ \sigma $$ by dividing both sides by $$ z $$:**
   $$
   \sigma = \frac{x - \mu}{z}
   $$

**Final Solution:**
$$
\sigma = \frac{x - \mu}{z}
$$
$$ \sigma = \frac{x - \mu}{z} $$

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