Question

The lemgth of time for one individuail to be serval ata caria isa nkm disribution with a moan of 4 minutes Yaperson goes to this caeteria r unch, what s the pebahily h he pse ià serve ss a minines h A person works Monday through Fridey and this persse has uncih at his caeria evey wk dy ha particular week, what is the prohability that Thursday is the 1 day ohe week in whih it nkes Ager h minutes to get served

Answer 1

Solution Griven time f be Saved lengtof let x at a Cateteni a x follous exponential distuvibution with am E minutes E() minates Nou the Probabili density function (paf) of exfomential distonibution given by is f(x) elseahene Cafeteia lunch is Sesved s less than to find Ca) Tf the oro bability thtthe Penion Pesnson 3 mintutes r(xc) f (a) d

P xe3) P(xec) - of 4 34 e fxca) -3 -ofp heLto f(xes) tenc the neuioied fiobabili ty is o-5216 0.s216 bTo find the frobability thetTh sday is h fiost daj than 3minute he Ceek fn Chick jt takes longei of to get Senved Rezuivned Poto bability LMendayTuesdady wednesdoy fonbabitity - took less than thaee minutes and Thursday took maetha 3minutes7

(x) (lxe) 0. 521x 0.516 X 0.527G x P 0.576 X0.5216 Xo.5216 X - O.5276 Xo.516 X o.576 X 5216 0-146 X 0.124 0.0694 ftence the eguited fhoba bility is "0.o64