Super Bowl XLVI was played between the New York Giants and the New England Patriots in Indianapolis. Due to a decade-long rivalry between the Patriots and the city's own team, the Colts, most Indianapolis residents were rooting heartily for the Giants. Suppose that 90% of Indianapolis residents wanted the Giants to beat the Patriots. What is the probability that, of a sample of 100 Indianapolis residents, at least 15% were rooting for the Patriots in Super Bowl XLVI?
A) 0.0300
B) 0.0478
C) 0.4763
D) 0.9525

Question

Quizplus · Accepted Answer

We can use the binomial distribution with n=100 and p=0.1 to find the probability of fewer than 15 people rooting for the Patriots.

P(X < 15) = binomcdf(100, 0.1, 14) ≈ 0.9522

Then, the probability of at least 15 people rooting for the Patriots is:

P(X ≥ 15) = 1 - P(X < 15) ≈ 0.0478

Therefore, the answer is B.

Super Bowl XLVI Was Played Between the New York Giants