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Question: 67% of LaGuardia students are female. A random sample of 6 students is to be selected. Let the random variable X be the number of female students in a sample.

a.) Explain why X is a binomial random variable. (Find the number of trials n, specify "success" and "Failure" outcomes, and identify p and q, probabilities of "success" and "failure" respectively.

b.) What is the probability that out of 6 randomly selected students at most 2 are male?

c.) What is the probability that out of 6 randomly selected students exactly 4 are female?

d.) Find the average number of female students per sample if a large number of random samples of 20 students were selected.

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