As of the end of the 2010 NFL season, Indianapolis Colts quarterback Peyton Manning, throughout his 13-year career, completed 65% of all of his pass attempts. Suppose the probability each pass attempted in the next season has probability 0.65 of being completed.
a. Does this mean that if we watch Manning throw 100 times in the upcoming season, he would complete exactly 65 passes? Explain.
b. Explain what this probability means in terms of observing him over a longer period, say for 1000 passes over the course of the next two seasons assuming Manning is still at his typical playing level. Would it be surprising if his completion percentage over a large number of passes differed significantly from 65%?