I like the "easy" and "certified" answer that can come from having some basic resources. Managers aren't going to understand algebra. You get 5 bullet points and can't say any math at all, but defend your assertion. I have been required to do this. If this is your question in a job interview, especially if the person asking the question doesn't have a math degree, then they want to see if you "speak human".
I would go to this site
I would type in the numbers, and select 'all confidence-interval methods', and hit "submit".
There are good guidelines for which method to use, but they all give a consistent number for the lower interval that does not include 50%.
A non-biased coin would include 50% in its confidence interval.
I would say "this is made by world-class PhD's in stats, and is a government facing AI in epidemiology", so without any other reason than this, we might still believe its numbers are good. Also, all the different methods agree.
I was asked in my interview "how many marbles do I need to draw from a bowl in order to make a pair, when there are two colors uniformly randomly distributed", and why.