Question

During his contract negotiations, the agent for an NFL wide receiver claims that his client is one of the most consistent performers in the league. To back up this claim, he states that his client has caught a pass in 40 of the last 42 games in which he has played. Given that the league-wide probability of catching at least one pass in a game is 0.80, is the receiver’s feat particularly unusual? Calculate (and plot) the probability of this occurrence. Should the team’s general manager be impressed?

Answer 1

The sample proportion here is given as: 40/42 = 0.9524

The z score for the given sample proportion is computed as:

From the standard normal tables, we get: P(Z > 2.47) = 0.0068

Therefore this is a highly unusual result ( we can see that even at 1% level of significance as 0.0068 < 0.01 ) Yes the team manager should be impressed. The value could be seen on the normal distribution plot as: