Question

H useysumpo U " AOC A second stage og alert has been called in a contain area of Los Angeles County in which there are 90 industrial firms. An inspector will visit 30 randomly selected firms to check for violations of regulations (a) of the firms are c ally violating at least one regulation, what is the pmf of the number of firms visited by the Inspector that are in violation of at least one regulation? O MX, 30, 0.4) Onix: 30,04) O x 30, 36, 90) O DO 30,04) O bx30, 30, 90) OBX30, 36,90) are in vion, approximate them of art (a) by () If there are 900 firms in the area, of which OM 30,100,000) • 30,04) Onix: 30,04) OMX, 30, 360,000) Onbox, 30, 360, 900) O x 30, 0.4) compute and both for the cact pm and the proximating in part (h). (Round your answers to two decal plac (c) For the number that are in violation among the 30 visited out of Computex and VX for the exact pent E(X) V = Compute X) and VX for the approximating pm. F(X) - 12 VIX) - 72

Answer 1

Solution from given data: N690 n 3o here we have to assume x' be the no of firms visited heve 'X' foltows the hypongeomehail disinibalion The hypergeorchaie distribution hixinink) (ka (NME nen ca The The pont of no of frimis visited that one on violation at least one regulation ; k=36 PlXzw = h (miwink) = (hew (MITH P(x=w)= [*; 890,30,36) = (3664] (*0-34 30-x) by using hypergeometric distribution we can get the .pmf of number of firms i >> h(x: 30/36190) So, the god option by . correct.

Given no. of thims an area : 900 (N) k. 360 h (tini nik) sh(X: 900/360.30) The probability (p) : K = 39.00 [P=0.4) On binomial dishaibukion approximation of Amf Parrca) by a simple pmf ♡:- blynp.6(x! 30,00 ini so. The end option f correct. (c) Pit Compute Eld) and wind for the exact amp? EC): na (M= k) = 30*0.4 EW. - 1 The vew value for Exact profis vw = n/M) * (1 - M ) & (N-0)/N-1

foom given data? Na 900 n=30 VWw= 30 *1*** *(1 - ) * (900-30.) 900 - 30*0.4 * 11-0.4) * 0.9677 =30* 4* 0-6*0.9677 6.97 = 6.967 1 V(x) = 6.97 lii] here we have to find out Elx) and vexed for the approximahing pdf! . Approximahing pdf means here we are wying here we are wing the binomi the binomial distribution Elt: nx po 330*04 TE(x)= 12 vCx) =nXP x1-P) :30 yoyx(1-04 12 0.6 VW - 7.2