Question

in a recent poll, the gallup organization found that 45% of adult americans believe that the overall state of moral values in the united states is poor. if a survey of a random sample of 15 adults in this country is conducted in which they are asked to disclose their feelings on the overall state of moral values, complete parts (a) through (g).

(a) explain why this is a binomial experiment. select all that apply.

□ a. each trial depends on the previous trial.

□ b. the experiment is performed until a desired number of successes are reached.

□ c. the experiment is performed a fixed number of times.

□ d. the trials are independent.

□ e. the probability of success is the same for each trial of the experiment.

□ f. there are three mutually exclusive possible outcomes, arriving on - time, arriving early, and arriving late.

□ g. the probability of success is different for each trial of the experiment.

□ h. there are two mutually exclusive outcomes, success (response that the state of moral values is poor) or failure (response that the state of moral values is not poor).

Explanation:

• Option C: A binomial experiment has a fixed number of trials. Here, the sample size is 15, so there are 15 trials (a fixed number).
• Option D: In a binomial experiment, trials are independent. When asking different adults about their feelings on moral values, one adult's response does not affect another's.
• Option E: The probability of success (an adult believing moral values are poor) is \(p = 0.45\) for each trial (each adult surveyed).
• Option H: A binomial experiment has two mutually - exclusive outcomes. Here, success is "believing the state of moral values is poor" and failure is "not believing the state of moral values is poor".

Answer:

C. The experiment is performed a fixed number of times.
D. The trials are independent.
E. The probability of success is the same for each trial of the experiment.
H. There are two mutually exclusive outcomes, success (response that the state of moral values is poor) or failure (response that the state of moral values is not poor).