Question

Write bimomial or Poisson: A particulr telephone mber is used to moelve both volce calls and fat mesages. Suppose that 25% of the incoming all involve fx mesages, and consider a imple of 25 incoming calls. What is te probability d aAtmot 6 of tdhe calle olea fa mge Eaty 6 of the calls ivolve a fax mge? At ast 6 of de calle ivolve a farmge? 4 More than 6 of de cals ivelve a fa message? The mber of regt forstence ecelved by a towing ervice Copute thn peobability that actly tn eqests ae oeived daringa particular 2-bour pariod &rthe oparators of dhe towing service take 30-min break for ach what is the probablity thet they do sot mis any calls for asistanoe How many calls would you epect during heir break has a Crtan difribchim i te a4 per hou Twenty percent of all telephones of a certain type are sub- mitted for service while under warranty. Of these, 60% can be repaired, whereas the other 40% must be replaced with new units. If a company purchases ten of these telephones, what is the probability that exactly two will end up being replaced under warranty? iLeaks oceur in a pipeline at a mean rate of I leak per 1,000 mesers In a 2500-meter section of pipe, what is the probability of (a) no leaks? (b) Three or more leaks? (c) Sketch the probability distribution. (d) What is the expected number of leaks? (e) Why not use the binomial? In proof testing of circuit boards, the probability that any particular diode will fail is .01. Suppose a circuit board con- tains 200 diodes. & How many diodes would you expect to fail, and what is the standard deviation of the mumber that are expected to fail? b What is the (approximate) probability that at least four diodes will fail on a rndomly selected board? e. If five boards are shipped to a particular customer, how likely is it that at least four of them will work properly? (A board works properly only if all its diodes work) The number of people arriving for treatment at an emer- gency room can be modeled byt parameter of five per hour. a. What is the probability that exactly four arrivals occur during a particular hour? b. What is the probability that at least four people arrive during a particular hour? c. How many people do you expect to arrive during a 45- min period? with a rate

Answer 1

D Bm n and p Binomial Because it contains n=25 P=0.25 & Poisson contain mean late it x = 4 ③ Binomial it contains n and p n= 10 P= 0.20 - Poisson mean rate it contains leak x=1 leak per 1000 3 Binomial it contains n and p n=200 diodes p=0.00 arrival eate Ô Poisson it contains mean x=5 per how...