Past exam of the year 1 of the computer science course of the University of Oxford / 2014 / Discrete mathematics, continuous mathematics and probability / 9 / b / ii / Solution

Let $X_i$ be the head indicator random variable for toss $i$. These are independent and identically distributed random variables with a Bernoulli distribution of parameter $1/2$, so $\mu =1/2$, $\sigma =1/2$, and $W=N/n$. Taking $h=1/5$ makes $h\sigma =1/10$. The preceding Chebyshev's inequality bound givesThe endpoints are included because this event is exactly $|W-1/2|\le 1/10$.