Giddy Up - Go is a hot new game app that can be downloaded on smartphones. Researchers wanted to know what proportion of smartphone users have downloaded the app. They believe that the actual proportion is $0.10$ and have decided to investigate.
After surveying a random sample of $225$ smartphone users, the researchers determined that $27$ had downloaded the app.
In constructing a confidence interval, which of the following shows how to calculate the standard deviation of the sample proportion?