A w apnns manu acrar uses a iquld pro allant that can at m x with ano r qui redu

Question

A w apnns manu acrar uses a iquld pro allant that can at m x with ano r qui reduca a en tar inatad far rdga A statist an ound that Zy cartridgAs ln tha na kilar o w ra contamnatad Letx be the number of cartridgcs samoed umt1a contaminated onc is found, t 15own that the probabity detribution for xgiven by the formula chown below. Complete parts a through c. 00 ou random samia v hnut F a Aman gun cart d es om th lor uni nu d non amina d one px)-(0.23)(077)"-1-1, 2.3 . Find prt) Interpret thia resut R1Round to three decimal places as needed.) Vha atha cintarrataion or p A. This vauc is the probabity that ons woud cncounter a contam nated cartridge on the first trial. 0 R Thia valua ia 'ha probablity tha'naweuil enoantera contaminated tilridgein t.na hindadtial® c. This vaue is the probabit, that ons would encounters non-contaminated cartridge on the first trial. b. Hndpi Intarpret this au B. This vaue is the probabity thal on woud firs: encourttr 5 uontamine tedcartridge non hundred trials. C. Ihls vaue ls the probabllty that ona would trat encoumar a non.contaminatad cartridge on tha tth trial c Find Pix 22) Intergrel tha esil Px2- Pix? 2-(Round to three cecimal places as needed.) Round to three decimal places as ncoded.) what tha int pratationtor P(x2 A. This vauc the probabilty that ons woud first encoumora contaminated cartridge on the second trial. C. Thiz aue ithe probabiity that on wu d firsencoumter a centaminsted cartridge on t leacne of the remairing tria's afer the fret was amempted.

Explanation / Answer

given P(X)=(.23)(.77)^x-1, X=1,2,3

a) p(x=1) = 0.23*0.77^(1-1) =0.23

option c

b)p(x=5)= 0.23*0.77^(5-1)=0.23*0.77^4 =0.080

option a

c) p(x>=2) = p(x=0)+p(x=1)+p(x=2)

p(x=o)=0.23*0.77^0-1 = 0.2987 +

p(x=1)=0.23 +

p(x=2)=0.23*0.77^2-1=0.1771   

p(x>=2)= 0.2987+0.23+0.1771 =0.7058

option c

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