CHAPTER 5 TEST FORM A

Transcription

1 94 Instructor s Rsourc Guid Undrstandabl Statistics, 8th Edition CHAPTER 5 TEST FORM A 1. Sam is a rprsntativ who slls larg appliancs such as rfrigrators, stovs, and so forth. Lt x = numbr of appliancs Sam slls on a givn day. Lt f = frquncy (numbr of days) with which h slls x appliancs. For a random sampl of 240 days, Sam had th following sals rcord. x f Assum th sals rcord is rprsntativ of th population of all sals day. (a) Us th rlativ frquncy to find P(x) for x = 0 to 7. (b) Us a histogram to graph th probability distribution of part (a). 1. (a) (b) (c) Comput th probability that x is btwn 2 and 5 (including 2 and 5). (d) Comput th probability that x is lss than 3. () Comput th xpctd valu of th x distribution. (f) Comput th standard dviation of th x distribution. (d) () (f) 2. Th dirctor of a halth club conductd a survy and found that 23% of mmbrs usd only th pool for workouts. Basd on this information, what is th probability that for a random sampl of 10 mmbrs, 4 usd only th pool for workouts? Of thos mountain climbrs who attmpt Mt. McKinly (Dnali), only 65% rach th summit. In a random sampl of 16 mountain climbrs who ar going to attmpt Mt. McKinly, what is th probability of ach of th following? (a) All 16 rach th summit. (b) At last 10 rach th summit. (c) No mor than 12 rach th summit. (d) From 9 to 12 rach th summit, including 9 and (a) (d)

2 Part III: Sampl Tsts, Chaptr 5 95 CHAPTER 5, FORM A, PAGE 2 4. A coach found that about 12% of all hocky gams nd in ovrtim. What is th xpctd numbr of gams nding in ovrtim if a random sampl of 50 hocky gams ar playd? Th probability that a truck will b going ovr th spd limit on I-80 btwn Chynn and Rock Springs, Wyoming is about 75%. Suppos a random sampl of 5 trucks on this strtch of I-80 ar obsrvd. (a) Mak a histogram showing th probability that r = 0, 1, 2, 3, 4, 5 trucks going ovr th spd limit. 5. (a) (b) Find th man µ of this probability distribution. (c) Find th standard dviation of th probability distribution. 6. Rcords show that th probability of catching a Northrn Pik ovr 40 inchs at Taltson Lak (Canada) is about 15% for ach full day a prson spnds fishing. What is th minimal numbr of days a prson must fish to b at last 83.3% sur of catching on or mor Northrn Pik ovr 40 inchs? W ar intrstd in whn th first six will occur for rpatd rolls of a balancd di. What is th population man for this gomtric distribution (i.., th xpctd numbr of rolls for th first 6 to occur)? 7.

3 96 Instructor s Rsourc Guid Undrstandabl Statistics, 8th Edition CHAPTER 5, FORM A, PAGE 3 8. Th probability that an airplan is mor than 45 minuts lat on arrival is about 15%. Lt n = 1, 2, 3, rprsnt th numbr of tims a prson travls on an airplan until th first tim th plan is mor than 45 minuts lat. (a) Writ a brif but complt discussion in which you xplain why th Gomtric distribution would b appropriat. Writ out a formula for th probability distribution of th random variabl n. (b) What is th probability that th 3 rd tim a prson flis, h or sh is on a flight that is mor than 45 minuts? (c) What is th probability that mor than thr flights ar rquird bfor a plan is mor than 45 minuts lat? 8. (a) 9. Suppos th avrag numbr of customrs ntring a stor in a 20 minut priod is 6 customrs. Th stor wants a probability distribution for th numbr of popl ntring th stor ach 20 minuts. (a) Writ a brif but complt discussion in which you xplain why th Poisson approximation to th binomial would b appropriat. Ar th assumptions satisfid? What is λ? Writ out a formula for th probability distribution of r. (b) What is th probability that xactly 3 customrs ntr th stor during a 20 minut priod? (c) What is th probability that mor than 3 customrs ntr th stor during a 20 minut priod? 9. (a) 10. Th probability a nw mdication will caus a bad sid ffct is Th nw mdication has bn givn to 150 voluntrs. Lt r b th random variabl rprsnting th numbr of popl who hav a bad sid ffct. (a) Writ a brif but complt discussion in which you xplain why th Poisson approximation to th binomial would b appropriat. Ar th assumptions satisfid? What is λ? Writ out a formula for th probability distribution of r. (b) Comput th probability that xactly 3 popl from th sampl of 150 voluntrs will hav a bad sid ffct from th mdication. (c) Comput th probability that mor than 3 popl out of th sampl of 150 voluntrs will hav a bad sid ffct from th mdication? 10. (a)

4 Part III: Sampl Tsts, Chaptr 5 97 CHAPTER 5 TEST FORM B 1. An aptitud tst was givn to a random sampl of 228 popl intnding to bcom Data Entry Clrks. Th rsults ar shown blow whr x is th scor on a 10 point scal, and f is th frquncy of popl with this scor. x f Assum th abov data rprsnts th ntir population of popl intnding to bcom Data Entry Clrks. (a) Us th rlativ frquncis to find P(x) for x = 1 to 10. (b) Us a histogram to graph th probability distribution of part (a). 1. (a) (b) (c) To b accptd into a training program, studnts must hav a scor of 4 or highr. What is th probability an applicant slctd at random will hav this scor? (d) To rciv a tuition scholarship a studnt nds a scor of 8 or highr. What is th probability an applicant slctd at random will hav such a scor? () Comput th xpctd valu of th x distribution. (f) Comput th standard dviation of th x distribution. (d) () (f) 2. Th managmnt of a rstaurant conductd a survy and found that 28 of th customrs prfrrd to sit in th smoking sction. Basd on this information, what is th probability that for a random sampl of 12 customrs, 3 prfrrd th smoking sction? Of all collg frshmn who try out for th track tam, th coach will only accpt 30%. If 15 frshmn try out for th track tam, what is th probability that (a) all 15 ar accptd? (b) at last 8 ar accptd? (c) no mor than 4 ar accptd? 3. (a)

5 98 Instructor s Rsourc Guid Undrstandabl Statistics, 8th Edition CHAPTER 5, FORM B, PAGE 2 (d) btwn 5 and 10 ar accptd (including 5 and 10)? (d) 4. Th prsidnt of a bank approvs 68% of all nw applications. What is th xpctd numbr of approvals if a random sampl of 75 loan applications ar chosn? Th probability that a vhicl will chang lans whil making a turn is 55%. Suppos a random sampl of 7 vhicls ar obsrvd making turns at a busy intrsction. (a) Mak a histogram showing th probability that r = 0, 1, 2, 3, 4, 5, 6, 7 vhicls will mak a lan chang whil turning. 5. (a) (b) Find th xpctd valu µ of this probability distribution. (c) Find th standard dviation of this probability distribution. 6. Past rcords show that th probability of catching a Lak Trout ovr 15 pounds at Talston Lak (Canada) us about 20% for ach full day a prson spnds fishing. What is th minimal numbr of days a prson must fish to b at last 89.3% sur of catching on or mor Lak Trout ovr 15 pounds? W ar intrstd in whn th first odd numbr will occur for rpatd rolls of a balancd di. What is th population man for this gomtric distribution (i.., th xpctd numbr of rolls for th first odd numbr to occur)? 7.

6 Part III: Sampl Tsts, Chaptr 5 99 CHAPTER 5, FORM B, PAGE 3 8. Past rcords at an applianc stor show that about 60% of th customrs who look at appliancs will buy on. Lt n = 1, 2, 3, rprsnt th numbr of customrs a sals clrk must hlp until th first sal of th day. (a) Writ a brif but complt discussion in which you xplain why th Gomtric distribution would apply in this contxt. Writ out a formula for th probability distribution of th random variabl n. (b) Comput P(n = 4). (c) Comput P(n 3). 8. (a) 9. At Community Hospital matrnity ward, babis arriv at an avrag of 8 babis pr hour. Th hospital staff wants a probability distribution for th numbr of babis arriving ach hour. (a) Writ a brif but complt discussion in which you xplain why th Poisson distribution would b appropriat. What is λ? Writ out a formula for th probability distribution. (b) What is th probability xactly 7 babis ar born during th nxt hour? (c) What is th probability that fwr than 3 babis ar born during th nxt hour? 9. (a) 10. As a tlcommunications satllit gos ovr th horizon, stord mssags ar rlayd to th nxt satllit which is still in position. Howvr, th probability is 0.01 that an intrruption will occur, and th rlay transmission will b lost. Out of 200 such rlays, lt r b th random variabl that rprsnt th numbr of transmissions that ar lost. (a) Writ a brif but complt discussion in which you xplain why th Poisson approximation to th binomial would b appropriat. Ar th assumptions satisfid? What is λ? Writ out a formula for th probability distribution of r. (b) Comput th probability that xactly two transmissions ar lost. (c) Comput th probability that mor than two transmissions ar lost. 10. (a)

7 100 Instructor s Rsourc Guid Undrstandabl Statistics, 8th Edition CHAPTER 5 TEST FORM C Writ th lttr of th rspons that bst answrs ach problm. 1. Th following data ar basd on a survy takn by a consumr rsarch firm. In this tabl x = numbr of tlvisions in houshold and % = prcntags of U.S. housholds. x or mor % 3% 11% 28% 39% 12% 7% A. What is th probability that a houshold slctd at random has lss than 3 tlvisions? 1. A. (a) 0.81 (b) 0.39 (c) 0.42 (d) 0.58 () 0.19 B. What is th probability that a houshold slctd at random has mor than 4 tlvisions? B. (a) 0.7 (b) 0.19 (c) 0.81 (d) 0.93 () 0.07 C. Comput th xpctd valu of th x distribution (round tlvisions of 5 or mor to 5). (a) 15 (b) 2.67 (c) 1.28 (d) 1.13 () 3.1 D. Comput th standard dviation of th x distribution (round tlvisions of 5 or mor to 5). (a) 15 (b) 2.67 (c) 1.28 (d) 1.13 () 3.1 C. D. 2. A mtorologist found from th past yar s rcords that it raind 17% of th days. Basd on this information, what is th probability that for a random sampl of 15 days, it raind 3 of thos days? (a) 0.17 (b) 0.67 (c) 0.28 (d) 0.13 () Of thos popl who los wight on a dit, 90% gain all th wight back. In a random sampl of 12 ditrs who hav lost wight, what is th probability of ach of th following? A. All 12 gain th wight back. 3. A. (a) 0.90 (b) (c) (d) () 10.8% B. At last 9 gain th wight back. B. (a) (b) (c) (d) 1.33% () C. No mor than 6 gain th wight back. C. (a) (b) (c) (d) () D. From 8 to 10 gain th wight back, including 8 and 10. D. (a) (b) 1.17% (c) (d) () 0.118

8 Part III: Sampl Tsts, Chaptr CHAPTER 5, FORM C, PAGE 2 4. Th managr of a suprmarkt found that 72% of th shopprs who tast a fr sampl of a food itm will buy th itm. What is th xpctd numbr of shopprs that will buy th itm if a random sampl of 50 shopprs tast a fr sampl? (a) 10 (b) 36 (c) 3 (d) 72 () Th probability that mrchandis stoln from a stor will b rcovrd is 15%. Suppos a random sampl of 8 stors, from which mrchandis has bn stoln, is chosn. A. Find th man µ of this probability distribution. 5. A. (a) 1.02 (b) 1.07 (c) 1.01 (d) 1.14 () 1.2 B. Find th standard dviation of th probability distribution. B. (a) 1.02 (b) 1.07 (c) 1.01 (d) 1.14 () Rcords show that th probability of sing a hawk migrating on a day in Sptmbr is about 35%. What is th minimal numbr of days a prson must watch to b at last 96.8% sur of sing on or mor hawks migrating? (a) 5 (b) 6 (c) 7 (d) 8 () W ar intrstd in whn th first six will occur for rpatd rolls of a balancd di. What is th population man for this gomtric distribution (i.., th xpctd numbr of rolls for th first 6 to occur)? 7. (a) 6 (b) 1 6 (c) 7 (d) 8 () 9 8. Rita is studying to b a ral stat agnt. About 61% of all popl who tak th licnsing xam pass. Lt n = 1, 2, 3, rprsnt th numbr of tims a prson taks th xam until th first pass. A. What is th formula for th probability distribution of th random variabl n. 8. A. (a) P(n) = (0.61) n (0.39) n 1 (b) P(n) = 0.39(0.61) n 1 (c) P(n) = 0.61(0.39) n 1 (d) P(n) = (0.61) n 1 (0.39) n () P(n) = (0.39) n B. What is th probability that Rita nds thr attmpts to pass th xam? B. (a) (b) (c) (d) () C. What is th probability that Rita nds mor than thr attmpts to pass th xam? C. (a) (b) (c) (d) () 0.907

9 102 Instructor s Rsourc Guid Undrstandabl Statistics, 8th Edition CHAPTER 5, FORM C, PAGE 3 9. Suppos th avrag numbr of customrs calling a tchnical support numbr in a 10-minut priod is 7 customrs. Th company wants a probability distribution for th numbr of popl calling ach 10 minuts. A. What is th formula for th Poisson probability distribution? 9. A. 7 r 7 (a) P( r ) = (b) P( r) 7! 7 r r = 7 r! 7 r 7! (c) P( r ) = (d) P( r ) = () P( r) 7 r r 7 r 7 = B. What is th probability that xactly 4 customrs call th support numbr during a 10 minut priod? (a) (b) (c) (d) () C. What is th probability that mor than 4 customrs call th support numbr during a 10 minut priod? (a) (b) (c) (d) () B. C. 10. Th probability that a manufacturd part at a plant is dfctiv is Th plant has manufacturd 300 parts. Lt r b th random variabl rprsnting th numbr of dfctiv parts. A. What is th formula for th Poisson approximation to th binomial probability distribution of r? 10. A. (a) ( ) 0.02 r ( 300 P r = ) (b) ( ) 0.02 r r 6 P r = (c) P( r) = (d) P( r) = () P( r) 6 r 6 B. What is th probability that xactly 5 parts ar dfctiv? B. (a) (b) (c) (d) () C. What is th probability that fwr than 2 parts ar dfctiv? C. (a) (b) (c) (d) () = 6 r! 6 r