II Ihl |I IF CHUOIIUI I Ul \\I II: ICUJI 3\"qu VJ III I6. 1) Ten students in a graduate program were randomly selected. Their grade point averages 1) (GPAs) when they entered the program were between 3.5 and 4.0. The following data were obtained regarding their GPAs on entering the program versus their current GPAs. Entering GPA (x) Current GPA (y) 3.5 3.6 3.8 3.7 3.6 3.9 3.6 3.6 3.5 3.9 3.9 3.8 4.0 3.7 3.9 3.9 3.5 3.8 3.7 4.0 2) A set of sample data consisting of 23 pairs of x and y values yields a sample linear 2) correlation coefficient of 0.747. At the 1% significance level. do the data provide sufcient evidence to conclude that x and y are linearly correlated? Find the critical tvalue and the sample t-value to support your answer it 3) Janet is planning to visit Arizona. New Mexico. and California on a 16-day vacation. If she plans to spend as much time in New Mexico as she does In the other two states combined. how can she allot her time In the three states? (Let x denote the number of days in Arizona. y the number of days in New Mexico, and z the number of days in California. Let 2 be the parameter.) A)x=B.y=8-z.Dssz B)x=z-B.y=8.Dssz C)x=8-z.y=8.05258 D)x=8.y=z-8.0-_=258 =ind the ratios of products A. B. and C using a closed model. 4) A B C A 0.2 0.3 0.1 B 0.3 0.1 0.8 C 0.5 0.6 0.1 A) 1: 149: 100 B) 33: 67: 63 C) t: 25: 25 D) 13:25: 100 5) A simplied economy is based on agriculture. manufacturing. and transportation. Each unit of agricultural output requires 0.3 unit of its own output, 0.5 of manufacturing. and 0.2 unit of transportation output. Each unit of manufacturing output requires 0.3 unit of its own output. 0.1 of agricultural, and 0.4 unit of transportation output. Each unit of transportation output requires 0.4 unit of its own output. 0.2 of agricultural, and 0.1 of manufacturing output. There is demand for 95 units of agricultural, 90 units of manufacturing. and 80 units of transportation output. How many units should each segment of the economy produce? A) Agriculture: 440: manufacturing: 555: transportation: 390 B) Agriculture: 555; manufacturing: 390; transportation: 440 C) Agriculture: 555; manufacturing: 440; transportation: 390 D) Agriculture: 390; manufacturing: 440; transportation: 555 5k b) A company manufactures two ballpoint pens. silver and gold. The silver requires 2 min in a grinder and 6 min In a bonder. The gold requires 7 min In a grinder and 8 min In a bonder. The grinder can be run no more than 54 hours per week and the bonder no more than 119 hours per week. The company makes a $6 prot on each sllver pen sold and $11 on each gold. How many of each type shouid be made each week to maximize prots? A) Silver pens: 0 B) Silver pens: 462 C) Sliver pens 4 D) Sliver pens: 3 Gold pens: 461 Gold pens: 4 Gold pens: 461 Gold pens: 462 7) An athlete uses three different exercise regimens for Increasing cardiovascular tness. An 7) 6) hour of regimen A rates a 3 In effectiveness. an hour of regimen B rates a 4 in effectiveness, and an hour of regimen C rates a 5 In effectiveness. In any given week. the athlete can train at most 3 hours by regimen A. In any given week the combined hours of regimens A and C may not exceed 8. In any glven week the combined hours of regimens B and C may not exceed 11. How many hours of each regimen should the athlete perform in a week In order to maximize the Increase In fitness? What is the maximumvalue obtained'f? Use a Venn diagram to answer the question. A) Agriculture: 440; manufacturing: 555; transportation: 390 13) Agriculture: 555; manufacturing: 390: transportation: 440 C) Agriculture: 555; manufacturing: 440: transportation: 390 D) Agriculture: 390; manufacturing: 440: transportation: 555 6) A company manufactures two ballpoint pens, silver and gold. The silver requires 2 min In a grinder 6) and 6 min In a bonder. The gold requires 7 min in a grinder and 8 min In a bonder. The grinder can be run no more than 54 hours per week and the bonder no more than 119 hours per week. The company makes a $6 profit on each silver pen sold and $11 on each gold. How many of each type should be made each week to maximize prots? / A) Silver pens: 0 B) Silver pens: 462 C) Sliver pens: 4 D) Sliver pens: 3 Gold pens: 461 Gold pens: 4 Gold pens: 461 Gold pens: 462 7) An athlete uses three different exercise regimens for Increasing cardiovascular fitness. An 7) hour of regimen A rates a 3 in effectiveness. an hour of regimen B rates a 4 in effectiveness. and an hour of regimen C rates a 5 In effectiveness. In any given week. the athlete can train at most 3 hours by regimen A. In any given week the combined hours of regimens A and C may not exceed 8. In any given week the combined hours of regimens B and C may not exceed 11. How many hours of each regimen should the athlete perform In a week in order to maximize the Increase In tness? What Is the maximumvalue obtained'i':t Use a Venn diagram to answer the question. 8) A survey of a group of 112 tourists was taken In St. Louis. The survey showed the 8) following: 62 of the tourists plan to visit Gateway Arch; \\ 49 plan to visit the zoo; 10 plan to visit the Art Museum and the zoo, but not the Gateway Arch; 12 plan to visit the Art Museum and the Gateway Arch. but not the 100: 18 plan to visit the Gateway Arch and the zoo, but not the Art Museum: 9 plan to visit the Art Museum. the zoo, and the Gateway Arch; 16 plan to visit none of the three places. How many plan to visit the Art Museum only? Use Bayes' rule to nd the indicated probability. 9) In one town, 7% of 18-29 year olds own a house, as do 34% of 30-50 year olds and 67% of 9) those over 50. According to a recent census taken in the town. 28.7% of adults In the town are 18 29 years old, 35.6% are 3050 years old, and 35.7% are over 50. What percentage of house- owners are 30- 50 years old