According to the Humane Society of the United States, there are approximately 77

Question

According to the Humane Society of the United States, there are approximately 77.5 million owned dogs in the United States, and approximately 40% of all U.S. households own at least one dog.† Suppose that the 40% figure is correct and that 15 households are randomly selected for a pet ownership survey. (a) What is the probability that exactly six of the households have at least one dog? (Round your answer to three decimal places.) (b) What is the probability that at most three of the households have at least one dog? (Round your answer to three decimal places.)

Explanation / Answer

p = 0.4

n = 15

This is a binomial distribution

P(X = x) = 15Cx * 0.4x * (1 - 0.4)15-x

a) P(X = 6) = 15C6 * 0.46 * 0.69 = 0.207

b) P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)

                   = 15C0 * 0.40 * 0.615 + 15C1 * 0.41 * 0.614 + 15C2 * 0.42 * 0.613 + 15C3 * 0.43 * 0.612

                   = 0.091

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