A Gallup poll of 1236 adults showed that 12% of the respondents believe that it is bad luck to walk under a ladder. Consider the probability that among 30 randomly selected people from 1236 who were polled, there are at least 2 who have that belief. Given that the subjects surveyed were selected without replacement, the events are not independent. Can the probability be found by using the binomial probability formula? Why or why not?
Yes. Although the selections are not independent, they can be treated as being independent by applying the 5% guideline.
No, the probability cannot be found using the binomial probability formula because the events are not independent. In a binomial experiment, the events must be independent, which means that the outcome of one event does not affect the outcome of another event.
In this case, the subjects were selected without replacement, meaning that once a person's belief is recorded, they are not available for selection again. Therefore, the probability of one person having the belief affects the probability of the next person having the belief.
To find the probability of at least 2 people out of 30 having the belief, you would need to use methods such as the hypergeometric distribution or simulation techniques that take into account the non-independence of the events.
No, the probability cannot be found using the binomial probability formula because the events in this scenario are not independent. In a binomial distribution, each trial is assumed to be independent of each other, meaning that the outcome of one trial does not affect the outcome of subsequent trials.
However, in this case, the subjects surveyed were selected without replacement, which means that the probability of selecting a person with a certain belief changes with each selection. As each person is selected, the total number of people in the sample decreases, thus affecting the probability of selecting someone with the belief.
To find the probability in this scenario, we need to use the hypergeometric probability formula. The hypergeometric distribution accounts for the lack of independence and allows us to calculate probabilities when sampling without replacement.