Question

An environmental engineer working for the EPA is tasked with observing water specimens from lakes in...

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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