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Working on a Percentile question
Question: A university wants to estimate the unknown 25-percentile height, pi0.25 (in cm), of its students. A random sample of 180 students is produced and the height of each student in the sample, Xi (i= 1,2, ... 180), is measured. The order statistics of Xi is denoted as Xi'. What is the level of confidence(in %) for X40<pi 0.25< 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] = C0.500.4(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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