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
a. a success is a pet owner who did not acquire their dog or cat from a shelter
b. a success is a pet owner who would not acquire their next dog or cat from a shelter
c. a success is a pet owner who acquired their dog or cat from a shelter.
d. a success is a pet owner who would acquire their next dog or cat from a shelter
b. for this binomial experiment, what is n?
n = 25
c. for this binomial experiment, what is p?
p = (round to one decimal place as needed.)

Explanation:

Step1: Recall binomial probability formula

The binomial probability formula is \(P(X = k)=C(n,k)\times p^{k}\times(1 - p)^{n - k}\), where \(n\) is the number of trials, \(p\) is the probability of success in a single trial.

Step2: Identify \(p\)

Given that half of all pet owners would get their next dog or cat from a shelter. So the probability of success (a pet owner who would acquire their next dog or cat from a shelter) \(p = 0.5\)

Answer:

\(p = 0.5\)