Question

according to a recent poll, half of all pet owners would get their next dog or cat from a shelter. consider a random sample of 25 pet owners and define x as the number of pet owners who would acquire their next dog or cat from a shelter. assume that x is a binomial random variable. complete parts a through f below.
a. for this binomial experiment, define a success.
oa. a success is a pet owner who did not acquire their dog or cat from a shelter.
ob. a success is a pet owner who would not acquire their next dog or cat from a shelter.
oc. a success is a pet owner who acquired their dog or cat from a shelter.
od. a success is a pet owner who would acquire their next dog or cat from a shelter.

Explanation:

In a binomial experiment, a success is defined based on the variable of interest. Here, \(x\) is defined as the number of pet owners who would acquire their next dog or cat from a shelter. So, a success should be in line with what \(x\) counts.

• Option A: Talks about not acquiring from a shelter, which is the opposite of what \(x\) (number of those who would acquire from a shelter) represents.
• Option B: Focuses on not acquiring next pet from a shelter, again contrary to \(x\)'s definition.
• Option C: Mentions acquired (past - tense), but the problem is about "would get their next" (future - oriented as per the poll context).
• Option D: Matches the definition of \(x\) (number of pet owners who would acquire their next dog or cat from a shelter).

Answer:

D. A success is a pet owner who would acquire their next dog or cat from a shelter.