Simple binomial test question

Hi, very simple I know, but just want to check that I think correctly.


the problem:
"A coin is tossed 10 times and 2 heads are obtained. Test Weather the coin
is biased."



So Definitely we are using binomial distribution, isnt it? so

null hypothesis: "We get 5 heads"

alternative hypothesis: "head number<>5"



So its gonna be 2-tailed test. So if I calculate propabilities to get 0,1,2
and add them I get the test value (which is about 0.054). But using 2-tailed
95% confidence level test, the first tail is located at 0.025 and the right
tail is at 0.975. Becouse 0.054 is more than 0.025 , the null hypothesis
remains, so we cannot say that the coin is biased.



Did it go ok?? this is how my common sense says it could be done. We cannot
use poison/normal distributions, couse sample size is small, isnt it?? We do
2-tailed or one tailed? I am sure 2-tailed, just checking ...



thanks


.