Question

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 the 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? choose the correct answer below.
a. yes. although the selections are not​ independent, they can be treated as being independent by applying the​ 5% guideline.
b. no. the selections are not​ independent, and the​ 5% guideline is not met.
c. yes. there are a fixed number of selections that are​ independent, can be classified into two​ categories, and the probability of success remains the same.
d. no. the selections are not independent.

Answer 1

The answer is a) although they are not independent, since they are less than 5% of the population, they can be treated as independent.