Solved: A university wants to estimate the unknown 25-percentile, Basic Computer Science

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A university wants to estimate the unknown 25-percentile

Working on a Percentile question

Question: A university wants to estimate the unknown 25-percentile height, pi_0.25 (in cm), of its students. A random sample of 180 students is produced and the height of each student in the sample, X_i(i= 1,2, ... 180), is measured. The order statistics of X_iis denoted as X_i'. What is the level of confidence(in %) for X₄₀0.25< X'₅₀?

So if I am applying the formula for the percentile correctly, which idk if i am, it should turn out something like

P[pi0.25] = C^0.50_0.4(1-0.25)²

Then from there try to calculate the confidence but I don't know what I can apply to find the CI

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Basic Computer Science: A university wants to estimate the unknown 25-percentile

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