Anita\'s, a fast-food chain specializing in hot dogs and garlic fries, keeps tra

Question

Anita's, a fast-food chain specializing in hot dogs and garlic fries, keeps track of the proportion of its customers who decide to eat in the restaurant (as opposed to ordering the food "to go"), so it can make decisions regarding the possible construction of in-store play areas, the attendance of its mascot Sammy at the franchise locations, and so on. Anita's reports that 45% of its customers order their food to go. If this proportion is correct, what is the probability that, in a random sample of 4 customers at Anita's, exactly 2 order their food to go? Round your response to at least three decimal places.

Explanation / Answer

This is binomial distribution problem, where P(X = r) = nCr*pr*(1-p)n-r
Given, p = 0.45, n = 4, r = 2

P(X = 2) = 4C2*0.452*(1-0.45)4-2 = 6*0.2025*0.3025 = 0.3675 = 0.368

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