MAT 326 Midterm with Solution, Fall 2011

1) (10 points) Among five applicants for chemical cogineering pesitian in a firm, scellent and the other three are rated a3 good. A manager ws lo interview. Find the probability that wo are rated a randomly chouses teu al these appli them a) the two rated as excellent. vices that sone et ho chaser two is alreads known ta ' Le ¥ 2) (28 points} An accounting tire tha reais Gime from a. consultir The weekly use given by (measurements in hours) oe ; ‘ — x" (4 =x Osxne4 Pledge a oes 0 “elsewhere a) Find the distribution function F(x) for weekly CPU ime. bh) Find the expected value and variance af weekly CPU time. “ ¢) The CPU time costs the fim $200 per how. Find the expected value and variance of the weekly cost for CPL time. d} In ihe coming 5 weeks. if we assume thatthe weekly CPU time is independent from week to week. find the probability that the weekly caster CPitime will exceed $600 exactly 2 limes. Oe Se ae See a | Gu é u om ™ < ne el ne ey ee 4 ; 5 ee F é a x le | “ mnie cee > Gs : =f ay eee a Be So ‘ — ; a oo bo : 5 ; yee’ ty 4 a> un ae pea ce a ey y (12 points) Relays ina section of an electrical circuit operate independently, and cach one clases properly when a switch is thrown with probability 0.5. the, following twa designs, cach involving four relays are presented fora section ofa. new circul F sos, find the probability of current fle 187 Be. Pe oe “d) (10 points} A type of capacitor has resistances that vary according to a normal distribution with a mean af 800 tneeahims and a standard deviation of 200 mepohms. A certain application specifies capacitors with resistances between 900 aid 1000 mezohms, : a) What proportion of these capacitors will meet his specificalon® bi If wo eapaciters are randomly chosen from a lotel capacitors ef this type, what is the probability that both will satis) the specification? KM. You Ver s me elo oe it 2. AG ve 5) (15 points) A geological study indicates thatan exploratery ofl well drilled in a certain rezion should strike ail with probability 0.2. ‘ind the probability usat the first strih 6) (25 points) Customer arrivals at a checkout outer in a department store have a paisson distributing, with aa average ef 6 customes per haut. a) For: hagit' en hour, find tee probabil: Ly that na merce tian Oye CueLoster arrive, b) Find the imenn fig the probability density finclion of the waiting time between the opening cf tne cotuite: ancl ile arrival af the liest custamer. c) If a clerk takes appre imately 15 minutes ta serve the he probability thal al least owaliting iwhen the service of the fi custo d) Find the mean. variane al time between | HTL