The 2014 AFL Championship game football tampering scandal, commonly referred to
ID: 3370758 • Letter: T
Question
The 2014 AFL Championship game football tampering scandal, commonly referred to as deflategate, or ballghazi is a controversy in the National football league (NFL) involving allegations of tampering with footballs by the New England Patriots, related to the accusations that the team tampered with the footballs used in the AFC Championship game against the Indianapolis Colts on January 18, 2015, a game the Patriots won 45-7.
NFL V.P. of officiating Dean Blandino explained that the 12.5 to 13.5 PSI range has been in place for decades, with no debate or analysis over whether the range should change.
Assume that the NFL footballs are inflated with an average PSI of 13.0 and a standard deviation of 0.30 PSI. Answer using excel.
(A) Calculate the probability of a football being inflated below the minimum 12.5 PSI range.
(B) Using your answer from (A) if the Patriots used 12 game balls, how many balls would you expected to be inflated below 12.5 PSI (excessively deflated)?
(C) From that game, it was found that 10 out of 12 Patriots balls were found to be underinflated. What is the probablity that a Patriots ball chosen at random
was underinflated?
(D) The 10 balls that were underinflated had PSI that were closer to 11.5 PSI. Calculate the z-score for 11.5 PSI.
(E) from your answers to questions a-d, do you believe that the Patriots tampered with the footballs from that game? Explain.
Explanation / Answer
here we use stanardard normal variate z=(x-mean)/sd
(A)for x=12.5, z=(12.5-13)/0.3=-1.6667
probability of a football being inflated below the minimum 12.5 PSI range=P(X<12.5)=P(Z<-1.6667)=0.0478
(B) required number=n*p=12*0.0478=0.5736
(C) What is the probablity that a Patriots ball chosen at random was underinflated=x/n=10/12=5/6=0.8333
(D) for x=11.5, z=(11.5-13)/0.3=-5
(E)yes, since 10 ball out of 12 are underinlated i.e.83.33% ball is underinflated which is more than typical 5%
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