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 XLVI?
A) 0.0092
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. The mean (μ) is np = 200 * 0.9 = 180, and the standard deviation (σ) is sqrt(np(1-p)) = sqrt(200 * 0.9 * 0.1) = 4.24. We want P(X < 170), which is P(Z < (170-180)/4.24) = P(Z < -2.36). Using the standard normal distribution table, this probability is approximately 0.0092.

Super Bowl XLVI Was Played Between the New York Giants