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 from a sample of 200 Indianapolis residents,fewer than 170 were rooting for the Giants in Super Bowl XLIV?
A) 0.0091
B) 0.0212
C) 0.4954
D) 0.9908

Question

Quizplus · Accepted Answer

The problem can be solved using the normal approximation to the binomial distribution. With p = 0.9 and n = 200, the mean is np = 180 and the standard deviation is sqrt(np(1-p)) = sqrt(18). We want P(X < 170), which is P(Z < (170-180)/sqrt(18)). Calculating this gives approximately 0.0091.

Super Bowl XLVI Was Played Between the New York Giants