Question

given the following statistical formula: $z = \frac{\bar{x}-\mu}{\frac{\sigma}{\sqrt{n}}}$ transpose the formula to solve $\sigma$ a. $\sigma = \frac{\bar{x}-\mu}{\frac{z}{\sqrt{n}}}$ b. none of these c. $\sigma = \frac{\bar{x}-\mu}{\frac{\sqrt{n}}{z}}$ d. $\sigma = \frac{z\times(\bar{x}-\mu)}{\sqrt{n}}\sqrt{n}$ e. $\sigma = \frac{\sqrt{n}(\bar{x}-\mu)}{z}$

Explanation:

Step1: Multiply both sides by $\frac{\sigma}{\sqrt{n}}$

$$Z\times\frac{\sigma}{\sqrt{n}}=\frac{\bar{x}-\mu}{\sqrt{n}}\times\frac{\sigma}{\sqrt{n}}\times\frac{\sqrt{n}}{\sigma}$$
$$Z\times\frac{\sigma}{\sqrt{n}}=\bar{x}-\mu$$

Step2: Multiply both sides by $\sqrt{n}$

$$Z\times\sigma = (\bar{x}-\mu)\times\sqrt{n}$$

Step3: Divide both sides by $Z$

$$\sigma=\frac{\sqrt{n}(\bar{x}-\mu)}{Z}$$

Answer:

E. $\sigma=\frac{\sqrt{n}(\bar{x}-\mu)}{Z}$