Man\'s Best Friend According to the Humane Society of the United States, there a

Question

Man's Best Friend 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 US. households own at least one dog.4 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 eight of the households have at least one dog? b. What is the probability that at most four of the households have at least one dog? c. What is the probability that more than 10 households have at least one dog?

Explanation / Answer

p = 0.4

n = 15

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

a) P(X = 8) = 15C8 * 0.48 * 0.67 = 0.118

b) P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4)

                  = 15C0 * 0.40 * 0.615 + 15C1 * 0.41 * 0.614 + 15C2 * 0.42 * 0.613 + 15C3 * 0.43 * 0.612 + 15C4 * 0.44 * 0.611

              = 0.217

c) P(X > 10) = P(X = 11) + P(X = 12) + P(X = 13) + P(X = 14) + P(X = 15)

                   = 15C11 * 0.411 * 0.64 + 15C12 * 0.412 * 0.63 + 15C13 * 0.413 * 0.62 + 15C14 * 0.414 * 0.61 + 15C15 * 0.415 * 0.60

                 = 0.009

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