A subcarrier is one telecommunication signal carrier that is piggybacked on top of another carrier so that effectively two signals are carried at the same time. Subcarriers are classified as data subcarriers (used for data transmissions), pilot subcarriers (used for channel synchronization), and null subcarriers (used for direct current). In the IEEE Journal of Oceanic Engineering (Apr. 2013), researchers studied the characteristics of subcarriers for underwater acoustic communications. Based on an experiment conducted off the coast of Martha's Vineyard (MA), they estimated that 25% of subcarriers are pilot subcarriers, 10% are null subcarriers, and 65% are data subcarriers. Consider a sample of 50 subcarriers transmitted for underwater acoustic communications.

a. How many of the 50 subcarriers do you expect to be pilot subcarriers? Null subcarriers? Data subcarriers?

b. How likely is it to observe 10 or more pilot subcarriers?

c. If you observe more than 25 pilot subcarriers, what would you conclude? Explain.