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- A group of medical professionals is considering theconstruction of a private clinic. If the medical de-mand is high (i.e., there is a favorable market for theclinic), the physicians could realize a net profit of$100,000. If the market is not favorable, they couldlose $40,000. Of course, they don’t have to proceedat all, in which case there is no cost. In the absenceof any market data, the best the physicians can guessis that there is a 50–50 chance the clinic will be suc-cessful. Construct a decision tree to help analyze thisproblem. What should the medical professionals do?Suppose insurance agency services customers who have both a homeowner’s policy and an automobile policy. For each type of policy, a deductible amount must be specified. For an automobile policy, the choices are TZS100 and TZS250, whereas for a homeowner’s policy, the choices are 0, TZS100, and TZS200. Suppose also that an individual is selected at random from the agency’s files. Let X = his deductible amount on the auto policy and Y = his deductible amount on the homeowner’s policy (a) What are the possible (X, Y) pairs? (b) Suppose the joint probability mass function is given by the insurance company in the accompanying joint probability in the following Table Table: Discrete Joint Probability Distribution for X and Y P(x,y) 0 100 200 X 100 0.2 0.10 0.2 250 0.05 0.15 0.3 What is p (100, 100) What is P (Y greater than 100)?Each airline passenger and his luggage must bechecked for security. Suppose that at GothamCity Airport, 3.6 passengers per minute arrive, onaverage. Also, assume that interarrival times areexponentially distributed. To check passengersfor security, the airport must have a checkpointconsisting of a metal detector and baggage X-raymachine. Whenever a checkpoint is in operation,two employees are required. These two employeeswork simultaneously to check a single passenger. Acheckpoint can check an average of 4.2 passengersper minute, where the time to check a passenger isalso exponentially distributed. Under the assumption that the airport has only one checkpoint, answer thefollowing questions.a. Why is an MyMy1, not an MyMy2, model relevanthere?b. What is the probability that a passenger will haveto wait before being checked for weapons?c. On average, how many passengers are waiting inline to enter the checkpoint?d. On average, how long will a passenger spend at thecheckpoint (including…
- An explosion at a construction site could haveoccurred as the result of static electricity, malfunctioningof equipment, carelessness, or sabotage. Interviews withconstruction engineers analyzing the risks involved ledto the estimates that such an explosion would occur withprobability 0.25 as a result of static electricity, 0.20 as aresult of malfunctioning of equipment, 0.40 as a result ofcarelessness, and 0.75 as a result of sabotage. It is alsofelt that the prior probabilities of the four causes of theexplosion are 0.20, 0.40, 0.25, and 0.15. Based on all thisinformation, what is(a) the most likely cause of the explosion;(b) the least likely cause of the explosion?The labels on boxes of Cheesy Poofs say that the box contains 16 ounces of Cheesy Poofs, but that doesn’tguarantee that each box contains exactly 16.00 ounces. The machine that fills the boxes doesn’t alwaysput out the exact same amount. The amount in each box is Normally distributed, and has a standarddeviation is .40 ounces. To help assure that most boxes contain as much or more than the label says, themachine is set so that the mean will be 16.28 ounces. What proportion of the boxes contain… d) …between 16.50 and 16.90 ounces? e) …between 16.50 and 19.00 ounces? f) …between 15.80 and 16.00 ounces?The labels on boxes of Cheesy Poofs say that the box contains 16 ounces of Cheesy Poofs, but that doesn’tguarantee that each box contains exactly 16.00 ounces. The machine that fills the boxes doesn’t alwaysput out the exact same amount. The amount in each box is Normally distributed, and has a standarddeviation is .40 ounces. To help assure that most boxes contain as much or more than the label says, themachine is set so that the mean will be 16.28 ounces. If you purchase 6 boxes of Cheesy Poofs,find the probability that the average amount (sample mean) in your six boxes is… c) …more than 16.50 ounces? d) …between 16.20 and 16.26 ounces?
- The labels on boxes of Cheesy Poofs say that the box contains 16 ounces of Cheesy Poofs, but that doesn’tguarantee that each box contains exactly 16.00 ounces. The machine that fills the boxes doesn’t alwaysput out the exact same amount. The amount in each box is Normally distributed, and has a standarddeviation is .40 ounces. To help assure that most boxes contain as much or more than the label says, themachine is set so that the mean will be 16.28 ounces. If you purchase 6 boxes of Cheesy Poofs,find the probability that the average amount (sample mean) in your six boxes is… a) …less than 16.00 ounces. b) … between 16.20 and 16.30 ounces? c) …more than 16.50 ounces?The labels on boxes of Cheesy Poofs say that the box contains 16 ounces of Cheesy Poofs, but that doesn’tguarantee that each box contains exactly 16.00 ounces. The machine that fills the boxes doesn’t alwaysput out the exact same amount. The amount in each box is Normally distributed, and has a standarddeviation is .40 ounces. To help assure that most boxes contain as much or more than the label says, themachine is set so that the mean will be 16.28 ounces. Complete the following sentences g) Half of the boxes of Cheesy Poofs produced which are labeled 16 ounces, actually contain more than____________________ounces. h) 14% of the boxes of Cheesy Poofs produced which are labeled 16 ounces, actually contain more than____________________ounces.The Collector’s Choice Inc. (CCI), a luxury car import company, has an old warehouse at the Port of Miami, Florida, where it temporarily stores expensive sports cars and automotive parts that arrive from Europe. This summer, CCI has noticed that the termite infestation in the warehouse has escalated to a point where tenting cannot be postponed anymore. (Tenting is the process of wrapping a building inside a huge tent that is subsequently filled with a poisonous gas capable of killing most forms of life inside, including insects, plants, pets, and human beings.) CCI’s pest control company’s contract specifies a to-do list of pre-tenting tasks, which include: Turning off all air-conditioning units and opening all windows of the warehouse Turning off all internal and external lights, including those operating on a timer Pruning all outdoor vegetation at least 18" away from the warehouse Soaking the soil around the warehouse on the first day of tenting The requirement of opening all…
- A researcher wants to explore the differences in health effects from two different types of sugar. She hypothesizes that artificial sweetener has lower long term health benefits than natural sugar. What is her null hypothesis? Fill in the blank. H0: μArtificalSweetener__________ μNaturalSugar Group of answer choices a) Less than b) Less than or equal to c) Greater than d) Greater than or equal toGulf Coast Electronics is ready to award contracts to suppliers for providing reservoir capacitors for use in its electronic devices. For the past several years, Gulf Coast Electronics has relied on two suppliers for its reservoir capacitors: Able Controls and Lyshenko Industries. A new firm, Boston Components, inquired into the possibility of providing a portion of the reservoir capacitors needed by Gulf Coast. The quality of products provided by Lyshenko Industries has been extremely high; in fact, only 0.5% of the capacitors provided by Lyshenko had to be discarded because of quality problems. Able Controls has also had a high quality level historically, producing an average of only 1% unacceptable capacitors. Because Gulf Coast Electronics has had no experience with Boston Components, it estimated Boston’s defective rate to be 10%. Gulf Coast would like to determine how many reservoir capacitors should be ordered from each firm to obtain 75,000 acceptable-quality capacitors to use…A study was conducted by researchers to determine if application of duct tape is more effective than cryotherapy (liquid nitrogen applied to the word for 10 seconds every 2 to 3 weeks) in the treatment of common warts. The researchers randomly divided 40 patients into two groups. The 20 patients group 1 had their warts treated treated by applying duct tape to the wart for 6.5 days and then removing the tape for 12 hours, at which point the cycke was repeated, for a maximum of 2 months. The 20 patients in group 2 had their warts treated by cryotherapy for a maximum of six treatments. Once the treatments were complete, it was determined that 17 patients in group 1 (duct tape) and 11 patients in group 2 (cryotherapy) had complete resolution of their warts. (Source: Archives of pediatrics and adolescent medicines, 156(10), 2002. conduct a hypothesis test to address the research question whether application of duct tape is more effective than cyrotherapy in the treatment of common warts.…