If a fair coin is flipped 400 times, the probability that fewer than 180 heads are obtained is approximately

If a fair coin is flipped 400 times, the probability that fewer than 180 heads are obtained is approximately equal to
a. 0.0228 b. 0.0000 c. 0.4207 d. 0.0793 e. 0. 0456

I know the answer is a, but I just can't seem to figure out how to get the answer, if anyone could help me out, it's much appreciated!

You have a binomial distribution with n = 400, p = 0.5, and q = 1 - p = 0.5. The mean of the distribution is

µ = np = 200

The standard deviation is

σ = √(npq) = √100 = 10

If we use the normal approximation to the binomial, then the z score for 180 is

z = (x - µ)/σ = (180 - 200)/10 = -2

From a normal distribution table we find that

p(z < -2) = 0.0228

So the answer is a)

The exact answer using the binomial distribution is 0.0201. The question asked for the approximate answer.

You'll want a calculator that can do a cumulative binomial distribution. You could also always use excel. You need to add (400Cn)*(.5^n)*(.5^(400-n)) from 0 to 179. When I used excel I got the answer to be 0.02011537. a is the closest answer to the answer that I got. None of the results I got matched your possibilities

No you have a 50 50 chance for it to land on heads and tails