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

(b) What is the probability that at most seven of the households have at least one dog? (Round your answer to three decimal places.)

(c) What is the probability that more than 10 households have at least one dog? (Round your answer to three decimal places.)

Explanation / Answer

We would be using binomial distribution in this case and the formula for the same is as mentioned below: -

n!/x!(n-x)!*p^x*q^n-x

Here, p=0.4 and hence q=0.6, n=15

a)

P(x=9)=0.06

b)

P(x=0)+P(x=1)+P(x=2)+P(x=3)+P(x=4)+P(x=5)+P(x=6)+P(x=7)=0.7868

c)

P(x=11)+P(x=12)+P(x=13)+P(x=14)+P(x=15)=0.0093

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