While waiting for the bus on a snowy morning, the expected waiting time (including unusual delays for snow!), is 12 minutes.
a. Use the Markov inequality to find an upper bound on the probability that the bus takes 15 minutes or more to arrive.
b. In the same scenario as above, assume that the standard deviation of the waiting time is 3. Use the Chebyshev inequality to find a bound on the probability that the bus takes between 6 to 18 minutes to arrive.