A sociologist surveyed 400 randomly selected college students and asked them if they had ever seen an episode of the original Star Trek series (from the 1960's). Of the 400 surveyed students, 84 of them said yes.

a. Construct a 95% confidence interval for the proportion of all college students who have seen an episode of the original Star Trek series. Show your work.

b. Interpret your interval from part (a) in the context of the problem.

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