Questions: The margin of error for a confidence interval in which the population standard deviation is known is: zc * (σ/√n) zc * (σ^2/n) zc * (σ^2/√n) zc * (σ/n)

Solution Steps

The margin of error for a confidence interval when the population standard deviation ($\sigma$) is known is given by: $$\text{Margin of Error} = z_{c} \cdot \frac{\sigma}{\sqrt{n}},$$ where:

• $z_{c}$ is the critical value corresponding to the desired confidence level,
• $\sigma$ is the population standard deviation,
• $n$ is the sample size.

The correct formula for the margin of error is: $$z_{c} \cdot \frac{\sigma}{\sqrt{n}}.$$ This matches the first option provided in the question.

The other options are incorrect because:

1. $z_{c} \cdot \frac{\sigma^{2}}{n}$ incorrectly squares $\sigma$ and divides by $n$ instead of $\sqrt{n}$.
2. $z_{c} \cdot \frac{\sigma^{2}}{\sqrt{n}}$ incorrectly squares $\sigma$.
3. $z_{c} \cdot \frac{\sigma}{n}$ incorrectly divides by $n$ instead of $\sqrt{n}$.

Final Answer