The variance of the number of heads in 16 tosses of a coin is
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 4
The number of heads follows a binomial distribution with n = 16 and \( p=q=\frac{1}{2} \).
\( \displaystyle \text{Variance}=npq=16\times\frac{1}{2}\times\frac{1}{2}=4 \)
Why the other options are incorrect
Option (1) 2 — Incorrect. This is the standard deviation, \( \sqrt{4}=2 \).
Option (3) 8 — Incorrect. This is the mean, np = 8, not the variance.
Option (4) 10 — Incorrect. The variance is 4, not 10.