Moderate# Combining Standard Deviations: Spinner

APSTAT-XYOZTY

Let $X$ represent the number where an arrow stops on a spinner that is numbered $1$ through $4$. The expected value of $X$ is $2.5$ and the standard deviation of $X$ is approximately $1.118$. The spinner will be spun twice, and the numbers the arrow stops on will be added.

Which of the following values is closest to the standard deviation of the resulting sum?