2. ÷ -/4 points DevoreStat93·E.074 My Notes A second-stage smog alert has been c

Question

2. ÷ -/4 points DevoreStat93·E.074 My Notes A second-stage smog alert has been called in a certain area of Los Angeles County in which there are 80 industrial firms. An inspector will visit 20 randomly selected firms to check for violations of regulations (a) If 24 of the firms are actually vlolating at least one regulatlon, what Is the pmf of the number of firms visited by the Inspector that are In vlolatlon of at least one regulatlon? b(x; 20, 24, 80) b(x; 20, 0.3) nb(x; 20, 24, 80) nb(x; 20, 0.3) h(x; 20, 0.3) h(x; 20, 24, 80) (b) If there are 800 firms In the area, of whlch 240 are In vlolatlon, approxlmate the pmf of part (a) by a slmpler pmf nb(x; 20, 0.3) b(x; 20, 240, 800) h(x; 20, 240, 800) h(x; 20, 0.3) nb(x; 20, 240, 800) b(x; 20, 0.3) (c) ForX = the number that are In vlolation among the 20 visited out of 800 firms, compute E(X) and V(X) both for the exact pmf and the approximating pmf in part (b). (Round your answers to two decimal places.) Compute E(X) and V(X) for the exact pmf E(X) = Compute E(X) and V(X) for the approximating pmf. E(X) = V(X) Need Help?Read It Talk to a Tutor

Explanation / Answer

a) being hypergeometric it should be h(x:20,24,80)

b)for binomial approximation: b(x:20,0.3)

c)E(X) =nk/N =20*240/800=6

V(X)=nk/N(1-k/N)*(N-n)/(N-1) =4.10

approximation

mean E(X) =np=20*0.3=6

V(X) =np(1-p) =20*0.3*0.7=4.2

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