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 20 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 five of the households have at least one dog? (Round your answer to three decimal places.)

Answer 1

Ans Let X be the number of households having atleast one dog.

Thus X in this problem follows binomial distribution with value of n = 20 and p = 0.4 such that the probability that X take a value k ranging from 0 to 20 is

P(X = k) =

Ans a The required probability that X is exactly equal to 6 is

P(X = 6) = = 0.1244 = 0.124 approximately

Ans b The required probability in this question is that there are atmost five of the households having at least one dog that is

P(X<=5) = P(X=0)+P(X=1)+P(X=2)+P(X=3)+P(X=4)+P(X=5)=

                

                 = 3.656 * 10^-5 + 4.875*10^-4 + 3.087 * 10^-3 + 0.0123 + 0.035 + 0.0746 = 0.1255 = 0.126 approximately