An environmental engineer working for the EPA is tasked with observing water specimens from lakes in northeast Georgia. In this region, each water specimen has a 10 percent chance of containing a particular organic pollutant.
(a) Treating each water specimen as a “trial,” suppose the three Bernoulli trial assumptions hold. State what this would imply (i.e., just give the assumptions for this situation).
(b) Let Y denote the number of specimens that contain the pollutant out of the next 15 analyzed. Plot the pmf and cdf of Y side by side.
(c) In part (b), find the probability that • there is exactly 1 polluted sample (Hint: use dbinom(y,n,p)) • there are 3 or more polluted samples (this event will trigger an EPA intervention). (Hint: use pbinom(y, n, p))
(d) In part (b), if the engineer found 10 or more of the 15 specimens to be polluted, what might be true?
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