Question 1

1.[6 marks] It is reported that only 45% of adults over the age of 30 can pass a basic fitness test. In order to further investigate this topic, a researcher selects a random sample of 18 adults over the age of 30 from across the country.

a)[2 marks] Does this process of selecting a random sample of 18 adults satisfy the "independent trials" requirement of the Binomial experiment? Explain your answer.

b)[2 marks] Assuming this is a proper Binomial experiment, find the mean number of adults that can pass the fitness test and provide an interpretation of its value in the context of the question.

c)[2 marks] Assuming that this is a proper Binomial experiment, what is the probability that at least 12 but less than 16 adults can pass the fitness test in the sample? Give your answer to four decimal places.