Suppose that an emergency medicine unit registers on the average 3 patients with paracot poisoning per week. Calculate the probability that in a given week the unit will register, (i) one or more cases of paracot poisoning, (ii) two or more cases but less than 5 cases of paracot poisoning
Let "X="the number of patients with paracot poisoning registered per week: "X\\sim Po(\\lambda t)."
Given "\\lambda t=3"
(i)
"=1-e^{-3}\\approx0.950213"
(ii)
"+P(X=4)=\\dfrac{e^{-3}(3)^2}{2!}+\\dfrac{e^{-3}(3)^3}{3!}+\\dfrac{e^{-3}(3)^4}{4!}"
"=e^{-3}(\\dfrac{9}{2}+\\dfrac{9}{2}+\\dfrac{27}{8})=\\dfrac{99e^{-3}}{8}\\approx0.616115"
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