Is it possible to use Markov inequality, as given in the following, to find bound on the probability over an interval?
$$P[X \ge a] \le \frac{E[X]}{a}$$
For example, consider this problem. The number of letters delivered by a postman during a day is a random variable X with expected value $E[X]=100$. So, can we use Markov inequality to find a lower bound on the probability that the number of letters delivered in a day lies between 75 and 125 i.e. $P[75\le X<125]$?
If variance is also available, Chebyshev inequality can be used for the above problem. However, in the absence of variance, can we use Markov inequality to find a bound on the probability over an interval?