Question

tested, the long-run percentage of defectives is 5% . Let X - the number of defective boards in a random sample of size n 20, so X - Bin(20, 0.05), (Round your probabilities to three decimal places.) When circuit boards used in the manufacture of compact disc players (a) Detemine PXs 2). (b) Determine PX 5). (c) Determine Pr1 s xs 4). (d) what is the probability that none of the 20 boards defectiva? deviation of X, (Raund vour standerd deviation to two decimal pleces.) exnected a pcted velue and s boards boards standard deylation

Answer 1

Given Data n20 X n Bin (20,0:05) p=0:05 g= lrp = 1r005 :0.95 Plx=x) = (6) p qux P(X52):- PCX52) = P(X=0) + P(x =1) +PCX=2) :-(41c,xorogº xo«p*(206,205*2048"] + [20.xoos+0296"] - [1*1 x 0.3585)+ (90x0.06x0.371] +[190 x 0.06%%0.347 = 0.3595 + 0.377 + 0.1886 -0.9241 [p(xsz) = 0.9241 b) P(x2): PCX5) = 1- P(XC4) Using Excel function Solver =Binom- Dost (x, trials, SP,C) - Bina.dist (4,20,0-05, 1) 099743 PLX 25) = 1-0.99743 P(x z5) - 0200257

c) P(i <x<4): Plisx54) = PSA)-plx=0); The e le ayan) - 20, Xovos kongea Solve P(x34) Ocel Function to Using Excel function to solve : = Binom. dist: (4,20,0.05,1) = 0.99743 = 0.99743 - 013585 -0.6389 Pll<x<4):= 016389) d) probability that none q the 20 beads is defective o- P(x - 1) - ( 3585. e) Expected value E(X), - np = 20X 0.05 -] board Standard deviationis esimpu - 420 20-0540.45 = Faqs = 0.97 5=0.92 boards