Finding a confidence interval of a ratio

[Angellargay]

I have absolutely no idea where I am getting stuck - but I'm in a thought loop and I can't seem to find my way out. I did a search on the forum but I have so thoroughly confused myself at this point that I spinning and nothing is making sense. Here's the problem:

A gentleman played 442 games of Klondike solitaire. He won 189 games out of those 442 games or approximately 42.76%. All I am trying to do is determine how to calculate a confidence interval for that 42.76%. Could anyone help? Please. Thank you.

 

[Harry_the_cat]

where p-hat = 0.4276 and n=442.

 

[Angellargay]

Thank you so much Harry! I now see where I was lost - z-values are constants...couldn't figure out how they were calculated. Incidentally, I came up with:

90% - 42.76% +- 3.87%
95% - 42.76% +- 4.61%
99% - 42.76% +- 6.07%

I'm not necessarily looking for confirmation - but if it looks very wrong, I'd be grateful if someone would alert me. Thank you again!