(Solution) - As part of a drug research study individuals suffering from -(2025 Original AI-Free Solution)

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As part of a drug research study, individuals suffering from arthritis take an experimental pain relief medication. Suppose that 25% of all individuals who take the new drug experience a certain side effect. For a given individual, let X be either 1 or 0, depending on whether s/he experienced the side effect or not, respectively.
a. If n = 3 people take the drug, find the probability distribution of the proportion who will experience the side effect.
b. Referring to part a, what are the mean and standard deviation of the sample proportion?
c. Repeat part b for a group of n = 10 individuals; n = 100. What happens to the mean and standard deviation of the sample proportion as n increases?