A coin is tossed 400 times and it shows head 220 times. Discuss whether the coin is unbiased or not.

No, the coin is biased

The correct answer is Option (2) → No, the coin is biased

Here $p=\frac{1}{2},q=\frac{1}{2},n=400$. We see that n is fairly large.

Expected value (Mean) = $np = 400 (\frac{1}{2})= 200$

and standard deviation = $σ = \sqrt{npq} =\sqrt{400.\frac{1}{2}.\frac{1}{2}}=10$

Observed value $220 = 200 + 2 (10) = Mean + 2σ$.

Hence, the coin is perhaps biased.