ENMGT 571Managerial Statistics I1.Exam ISolve the following problems:I. A computer rating service is commissioned to rank 10 different brands of flatscreen LCD monitors. The rating service is to rank the top three brands inorder 1 through 3 (12 points)a) In how many different ways can the computer rating service arriveat the final ranking?b) If the rating service can distinguish no difference among thebrands and therefore arrives at the final ranking by chance whatis the probability that one particular brand (call it Company Z sbrand) is ranked first?c) Suppose that the computer rating service is to choose the topthree from the group of 10 but is not to rank the three? In howmany different ways can the rating service choose the three to bedesignated top of the line flat screen LCD monitorsd) Consider the same information as part c and assume the ratingservice makes its choice by chance. Say there is a company(company X) that has two brands in the group of 10. What is theprobability that one of company s X brands is selected in the topthree?II. An experimenter is studying the effects of temperature pressure and type ofcatalyst on yield from a certain chemical reaction. Three differenttemperature four different pressures and five different catalysts are underconsideration: (12 points)a) If any particular experimental run involves the use of a singletemperature pressure and catalyst how many experimental runsare possible?b) How many experimental runs are there that involve use of thelowest temperature and two lowest pressures along with the fivecatalyst?c) Suppose that five different experimental runs are to be made onthe first day of experimentation. If the five are randomly selectedfrom among all the possibilities so that any group of five has thesame probability of selection what is the probability that adifferent catalyst is used on each run?ENMGT 571Managerial Statistics IIII.Exam IA mathematics professor wishes to schedule an appointment with each ofher eight teaching assistants four men and four women to discuss hercalculus course. Suppose all possible orderings of appointments are equallylikely to be selected. (15 points)a) What is the probability that at least one female assistant is amongthe first three of whom the professor meets?b) What is the probability that after the first five appointments she hasmet with all female assistants?IV.A real estate agent has 8 master keys to open several new homes. Only 1master key will open any given house. If 40% of these homes are usuallyleft unlocked (10 Points)a) what is the probability that the real estate agent can get into aspecific home if the agent selects 3 master keys at random beforeleaving the office?V.The US Army Corps of Engineers study on the DDT contamination of fishin the Tennessee River (Alabama) revealed the following: 52 percent of thefish are found between 275 and 300 miles 39% are found between 305 and325 miles and 9% are found between 330 and 350 miles (10 points)a) Given that a contaminated fish is found in a certain distanceupstream the probability that it is a channel catfish (CC) isdetermined from the data as P(CC/275-300)=.775P(CC/305-325) = .77 and P(CC/330-350) =.86. If a contaminatedcatfish is captured from the Tennessee River what is theprobability that it was captured 275-300 miles upstream?b) What is the probability of being a channel catfish (CC)?2.A box in a certain supply room contains eleven 40-W light bulbs and nine 75-Wbulbs. Suppose that three bulbs are randomly selected(15 pts)a. What is the probability that exactly two of the of the selected bulbs are rated 75W?b. What is the probability that at least one 40W bulb is selected?c. Given a 40-W bulb is selected on the first draw what is the probability ofselecting exactly one more 40-W?ENMGT 571Managerial Statistics I3.Exam IA market study taken at a local sporting goods store showed that of 30 peoplequestioned 18 owned tents 15 owned sleeping bags 14 owned camping stoves6 owned both tents and camping stoves and 10 owned both sleeping bags andcamping stoves: (15 pts)a. What is the probability of owning a tent owning a camping stove owninga sleeping bag owning both a tent and a camping stove and owning botha sleeping bag and a camping stove?b. What is the probability of owning a tent or a camping stove?c. What is the probability of owning neither a camping stove or a tentd. Given a person questioned owns a tent what is the probability he alsoowns a camping stove?e. Are the events of owning a tent and owning a camping stove mutuallyexclusive? Explain briefly?f. Are the events of owning a sleeping bag and owning a camping stoveindependent? Explain Briefly?g. If four people questioned owned a tent a sleeping bag and a campingstove then up to how many can own only a camping stove?4.A regional telephone company operates three identical relay stations atdifferent locations. During a one-year period the number of malfunctionsreported by each station and the causes are shown below. (11 pts)______Stations:Problems with electricity suppliedComputer malfunctionMalfunctioning electrical equipmentCaused by other human errorsA6457B1449C___1215a. What is the probability of a Computer Malfunction?b. What is the probability that station A will experience malfunctionwith electrical equipment?c. Suppose (given) that a malfunction was reported and it wasfound to be caused by other human errors. What is theprobability that it came from station C?d. Given we have a problem at station B What is the probabilitythat it is a problem other than a computer malfunction?Level of Detail: Show all workOther Requirements: Please answer questions and show all work for 1 (I II III IV V) and 2 (a b c). I already have completed 3 and 4.

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