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1. Let Y,,denote the nth order statistic of a random sample of size n from a distribution of the continuous type. Find th smallest value of n for which Pr (eo.9 <>Y,,) > 0.75.
2. Let Y1 <>Y2 <>Y3 <>Y4 <>Y5 denote the order statistics of a random sample of size 5 from a distribution of the continuous type. Compute:
(a) Pr ( Y, ,o5 Y5).
(b) Pr ( Y, ,o.25 Y3).
(c) Pr ( Y4 ,o.so Ys).
(a) Set up a 99% confidence interval estimate of the true population average amount of paint included in a five-litre can. (Use the z-table.) (b) Based on the results of (a), do you think that the store owner has a right to complain to the manufact..
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