If a 99% confidence interval states that the population mean is greater than 100 and less than 400. Then the sample mean and margin of error respectively are:

250, 150

The correct answer is Option (1) → 250, 150

Given 99% confidence interval: $100 < \mu < 400$

Confidence interval formula: $\bar{x} \pm E$, where $\bar{x}$ is sample mean and $E$ is margin of error.

Lower limit = $\bar{x} - E = 100$

Upper limit = $\bar{x} + E = 400$

Adding the two equations: $(\bar{x} - E) + (\bar{x} + E) = 100 + 400 \Rightarrow 2\bar{x} = 500 \Rightarrow \bar{x} = 250$

Margin of error: $E = \bar{x} + E - \bar{x} = 400 - 250 = 150$