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) 0.0475
C) 0.4763
D) 0.9525

Question

Quizplus · Accepted Answer

This problem involves calculating the probability of at least 15 out of 100 Indianapolis residents rooting for the Patriots, given that 90% of residents were rooting for the Giants. This scenario can be modeled using a binomial distribution with n = 100 and p = 0.1 (the probability of rooting for the Patriots).

Using a binomial calculator or software, we can find the probability of getting at least 15 Patriot supporters in a sample of 100, given p = 0.1:

P(X≥15) = 1 - P(X<15) = 1 - binomcdf(100, 0.1, 14) = 0.0475

where binomcdf is the cumulative distribution function for a binomial distribution.

Therefore, the probability of at least 15% (or 15 out of 100) Indianapolis residents rooting for the Patriots is 0.0475, which is closest to choice (B).

Super Bowl XLVI Was Played Between the New York Giants