05 Answer Key - Solutions 1(a) Hyper geometric N,S,n,K : 65...

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Solutions 1(a) Hyper geometric N,S,n,K : 65 10 5 0 P(K=0| N, S, n) = C(10, 0) C(55, 5) / C(65, 5)= 1*3478761 / 8259888 = 0.4212 1 Hypogeum, 1 params, 1 setup, 1 answer. Also possible by 55/65 * 54/64 * 53/63 * 52/62 * 51/61= 0.421163216740953 (b1) Binomial (1) n=7, p=.12 (1) P(K=0 | n, p) = (1-p)^n = 0.40867559636992 1 + 1 marks (b2) 1 - P(0) - P(1) = 1 - 0.40867559636992 - 0.39009943289856 = 0.20122497073152 1 setup, 1 parts, 1 answer (c) P(K<12 | n=198, p=.12) ~= P(z < (11.5 - np) /sqrt(npq) = P(z < -2.68117965919122 ) but use z = -2.68 to get 0.00368110800917498 or 0.37 % probability 1 setup, 1 CC, 1 z, 1 lookup, 1 answer (d) Must reduce std deviation of "K" by using FPC, so z gets bigger. FPC = sqrt((N-n)/(N-1)) = 0.799082042153209 1 mark z --> -3.35532463220735 use -3.55 giving Prob .00019 1 mark 2. (a) W = 1225*N+3543*Z E(W)= 1225*23.45+3543*31.23= 139374.14 $ (1 mark) V(W)=(1225^2)*(1.29^2)+(3543^2)*(2.45^2)+2*1225*3543*1.29*2.45*(-0.4)= (1 mark) 66871967.715 $^2 ==> SD(W)= 8177.52821548174 $ (1 mark) CV(W) = sd/mean= 0.0586732102202155 (1 mark)
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05 Answer Key - Solutions 1(a) Hyper geometric N,S,n,K : 65...

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