I met a question about probability, it seems easy but I got stuck. The question is:
Suppose there is an unfair coin, the HEAD probability is $p=0.7$.
(Q1) If we toss the coin for 100 times, what is the expectation and the variance of this experiment?
(Q2) Answer with reason whether or not the probability is higher than $1/10$ that the number of HEAD appear times is less than $50$ as we toss the coin for $100$ times.
Q1 is easy, I know expectation is $n*p=70$ and variance is $n*p*(1-p)=21$. But for Q2 I have no idea.
At first I think it looks like... a sample distribution of sample mean used in statistics but... I don't know whether (or how) it will obey a normal distribution.
Then I also try to calculate the sum of $P(H=0)+P(H=1)+...+P(H=50)$, but the work is huge, even I use an approximation of Passion distribution...
So could you share some of your thought? Thank you!