LARSON CALCULUS Ch09 Probability and Calculus

1. A icoin iis itossed ifive itimes. iDescribe ithe ievent iA ithat iat ileast ifour itails ioccur. A) B) C) D) E) Ans: C 2. Three ipeople iare iasked itheir iopinions ion ia ipolitical iissue. iThey ican ianswer i"Opposed" i(O) ior i"Undecided" i(U). iFind ithe isample ispace iS. A) B) C) D) E) Ans: E 3. A icard iis ichosen iat irandom ifrom ithree i52-card idecks iof istandard iplaying icards i. iWhat iis ithe iprobability ithat ithe icard iwill ibe iblack iand ia iface icard? iA iface icard iis ia iking, ia iqueen, ior ia ijack. A) B) C) D) E) Ans: B 4. Determine iwhether ithe itable irepresents ia iprobability idistribution. A) no B) yes Ans: A 5. Sketch ia igraph iof ithe iprobability idistribution. 0 1 2 3 4 A) B) C) D) E) Ans: D 6. Find i igiven ithe iprobability idistribution. i 0 1 2 3 4 5 0.047 0.185 0.240 0.325 0.159 0.044 A) 0.159 B) 0.797 C) 0.203 D) 0.956 E) 0.044 Ans: D 7. Find i igiven ithe iprobability idistribution. i 0 1 2 3 0.029 0.181 0.440 0.350 A) 0.440 B) 1.000 C) 0.790 D) 0.650 E) 0.250 Ans: D 8. Estimate ithe ivariance ifor ithe ifollowing iprobability idistribution ito itwo idecimal iplaces. A) B) C) D) E) 1.00 Ans: B 9. Find ithe istandard ideviation i ifor ithe ifollowing iprobability idistribution. iRound iyour ianswer ito ithree idecimal iplaces. 1 2 3 4 5 A) 2.600 B) 1.562 C) 5.954 D) 2.440 E) 1.612 Ans: B 10. Find ithe iexpected ivalue for ithe ifollowing iprobability idistribution. iRound iyour ianswer ito ithree idecimal iplaces. 5,000 2,500 300 0.014 0.062 0.924 A) 7.225 B) 904.398 C) 2,724.840 D) 817,935.160 E) 52.200 Ans: E 11. A ipublishing icompany iintroduces ia inew iweekly imagazine ithat isells ifor i$4.69 ion ithe inewsstand. iThe imarketing igroup iof ithe icompany iestimates ithat isales ix i(in ithousands) iwill ibe iapproximated iby ithe ifollowing iprobability ifunction. iFind ithe iexpected irevenue. iRound iyour ianswer ito ithe inearest idollar. 10 15 20 30 40 0.24 0.29 0.23 0.10 0.14 A) 93,565 B) 94 C) 456 D) 19,950 E) 456,091 Ans: A 12. An iinsurance icompany ineeds ito idetermine ithe iannual ipremium irequired ito ibreak ieven ion ifire iprotection ipolicies iwith ia iface ivalue iof i 90,000. iIf ix iis ithe iclaim isize ion ithese ipolicies iand ithe ianalysis iis irestricted ito ithe ilosses i 30,000, i 50,000, iand i 90,000, ithen ithe iprobability idistribution iof ix iis ias ishown iin ithe itable. iWhat ipremium ishould icustomers ibe icharged ifor ithe icompany ito ibreak ieven? iRound iyour ianswer ito ithe inearest idollar. 0 30,000 50,000 90,000 0.9910 0.0036 0.0009 0.0045 A) 553 B) 24 C) 42,500 D) 558 E) 62,000 Ans: D 13. If ix iis ithe inet igain ito ia iplayer iin ia igame iof ichance, ithen iE(x) iis iusually inegative. iThis ivalue igives ithe iaverage iamount iper igame ithe iplayer ican iexpect ito ilose iover ithe ilong irun. iA iservice iorganization iis iselling i$2 iraffle itickets ias ipart iof ia ifundraising iprogram. iThe ifirst iprize iis ia iboat ivalued iat i$2920, iand ithe isecond iprize iis ia icamping itent ivalued iat i$600. iIn iaddition ito ithe ifirst iand isecond iprizes, ithere iare itwenty-two i$20 igift icertificates ito ibe iawarded. iThe inumber iof itickets isold iis i3000. iFind ithe iexpected inet igain ito ithe iplayer ifor ione iplay iof ithe igame. iRound iyour ianswer ito ithe inearest icent. A) 1178.00 B) 1.47 C) 0.68 D) –$0.68 E) –$1178.00 Ans: D 14. A ibaseball ifan iexamined ithe irecord iof ia ifavorite ibaseball iplayer’s iperformance iduring ihis ilast i50 igames. iThe inumbers iof igames iin iwhich ithe iplayer ihad izero, ione, itwo, ithree, iand ifour ihits iare irecorded iin ithe itable ishown ibelow. iFind ithe istandard ideviation i . iRound iyour ianswer ito itwo idecimal iplaces. Number iof ihits 0 1 2 3 4 Frequency 10 22 5 12 1 A) 1.44 B) 1.12 C) 1.55 D) 1.25 E) 1.20 Ans: B 15. Find ithe iconstant ik isuch ithat ithe ifunction i iis ia iprobability idensity ifunction iover ithe iinterval i . A) 5 B) C) D) E) Ans: B 16. Find ithe ivalue iof ithe iconstant ia ithat imakes ithe igiven ifunction ia iprobability idensity ifunction ion ithe istated iinterval. i i i A) B) C) D) E) 1 Ans: C 17. Find ithe iconstant such ithat ithe ifunction is ia iprobability idensity ifunction iover ithe iinterval . A) 1 B) C) D) E) Ans: E 18. Sketch ithe igraph iof ithe iprobability idensity ifunction i iover ithe iinterval i . A) B) C) D) E) Ans: B 19. For ithe iprobability idensity ifunction i ion ithe iinterval i , ifind ithe iprobability ithat i . iRound iyour ianswer ito ithe inearest ihundredth. A) 0.07 B) 0.83 C) 0.97 D) 0.09 E) 0.06 Ans: C 20. For ithe iprobability idensity ifunction ion ithe iinterval i ifind ithe iprobability ithat i . iRound iyour ianswer ito ithe inearest ihundredth. A) 0.15 B) 0.67 C) 0.78 D) 0.33 E) 0.12 Ans: C 21. For ithe iprobability idensity ifunction i ion ithe iinterval i , ifind ithe iprobability ithat i . iRound iyour ianswer ito ithe inearest ithousandth. A) 0.088 B) 0.245 C) 0.224 D) 0.250 E) 0.264 Ans: E 22. Buses iarrive iand idepart ifrom ia icollege ievery i40 iminutes. iThe iprobability idensity ifunction ifor ithe iwaiting itime it i(in iminutes) ifor ia iperson iarriving iat ithe ibus istop iis i ion ithe iinterval i . iFind ithe iprobability ithat ithe iperson iwill iwait ino ilonger ithan i20 iminutes. A) B) C) D) E) Ans: C 23. The idaily idemand ifor igasoline i(in imillions iof igallons) iin ia icity iis idescribed iby ithe iprobability idensity ifunction iover ithe iinterval i . iFind ithe iprobability ithat ithe idaily idemand ifor igasoline iwill ibe iat ileast i3 imillion igallons. A) 0.444 B) 0.111 C) 0.174 D) 0.340 E) 0.250 Ans: E 24. The itime it i(in ihours) irequired ifor ia inew iemployee ito isuccessfully ilearn ito ioperate ia imachine iin ia imanufacturing iprocess iis idescribed iby ithe iprobability idensity ifunction i iover ithe iinterval i . iFind ithe iprobability ithat ia inew iemployee iwill ilearn ito ioperate ithe imachine iin imore ithan i2 ihours ibut iless ithan i5 ihours. A) 0.4498 B) 0.1264 C) 0.3714 D) 0.0981 E) 0.2733 Ans: C 25. A imeteorologist ipredicts ithat ithe iamount iof irainfall i(in iinches) iexpected ifor ia icertain icoastal icommunity iduring ia ihurricane ihas ithe iprobability idensity ifunction i i i . iFind iand iinterpret ithe iprobability . A) 90% iprobability iof ireceiving iup ito i13 iinches iof irain B) 96% iprobability iof ireceiving iup ito i13 iinches iof irain i C) 98% iprobability iof ireceiving iup ito i13 iinches iof irain D) 4% iprobability iof ireceiving iup ito i13 iinches iof irain E) 10% iprobability iof ireceiving iup ito i13 iinches iof irain Ans: B 26. Sketch ithe igraph iof ithe ifollowing iprobability idensity ifunction iand ilocate ithe imean ion ithe igraph. i i A) mean i: 1.5 B) mean i: 2.0 C) mean i: 4.0 D) mean i: 3.0 E) mean i: 4.0 Ans: C 27. Sketch ithe igraph iof ithe ifollowing iprobability idensity ifunction iand ilocate ithe imean ion ithe igraph. i i i A) mean i: 1.600 B) mean i: 2.012 C) mean i: 0.555 D) mean i: 1.848 E) mean i: 0.714 Ans: B 28. For ithe igiven iprobability idensity ifunction, ifind i i i i A) 12.000 B) 6.400 C) 9.000 D) 5.400 E) 28.800 Ans: D 29. Find ithe imedian iof ithe iexponential iprobability idensity ifunction i iover ithe iinterval i . A) 1.213 B) 0.693 C) 0.396 D) 1.061 E) 0.875 Ans: C 30. Find ithe imean, ivariance, iand istandard ideviation iof ithe iuniform idistribution i iover ithe iinterval i[0, i8] iwithout iusing iintegration. i A) expected ivalue mean : 4.000 variance: 5.333 standard ideviation: 2.309 B) expected ivalue mean : 5.333 variance: 4.000 standard ideviation: 2.309 C) expected ivalue mean : 5.333 variance: 2.309 standard ideviation: 4.000 D) expected ivalue mean : 2.309 variance: 4.000 standard ideviation: 5.333 E) expected ivalue mean : 4.000 variance: 2.309 standard ideviation: 5.333 Ans: A 31. If i iis ian iexponential irandom ivariable iwith ithe iprobability idensity ifunction i ifind i A) B) C) D) E) 1 Ans: C 32. Find ithe imean, ivariance, iand istandard ideviation iof ithe inormal idensity ifunction i iover i . iDo inot iuse iintegration. A) expected ivalue mean : 4 variance: 36 standard ideviation: 6 B) expected ivalue mean : 36 variance: 4 standard ideviation: 6 C) expected ivalue mean : 36 variance: 6 standard ideviation: 4 D) expected ivalue mean : 6 variance: 4 standard ideviation: 36 E) expected ivalue mean : 4 variance: 6 standard ideviation: 36 Ans: A 33. Let be ia irandom ivariable ithat iis inormally idistributed iwith ithe igiven imean i iand istandard ideviation i . iFind ithe iprobability i iusing ia isymbolic iintegration iutility. iRound iyour ianswer ito ifour idecimal iplaces. A) 0.1908 B) 0.3085 C) 0.2525 D) 0.1695 E) 0.0763 Ans: B 34. Let be ia irandom ivariable ithat iis inormally idistributed iwith ithe igiven imean i iand istandard ideviation i . iFind ithe iprobability i iusing ia isymbolic iintegration iutility. A) 0.5889 B) 0.6687 C) 0.7970 D) 0.6302 E) 0.5292 Ans: C 35. The iarrival itime it iof ia ibus iat ia ibus istop iis iuniformly idistributed ibetween i A.M. iand i A.M. iWhat iis ithe iprobability ithat iyou iwill imiss ithe ibus iif iyou iarrive iat ithe ibus istop iat i A.M.? iRound iyour ianswer ito itwo idecimal iplaces. A) 0.25 B) 0.67 C) 0.36 D) 0.33 E) 0.57 Ans: A 36. iThe idaily idemand i ifor ia icertain iproduct i(in ihundreds iof ipounds) iis ia irandom ivariable iwith ithe iprobability idensity ifunction i i iover ithe iinterval i . iFind ithe iprobability ithat i iis iwithin ione istandard ideviation iof ithe imean. iExpress iyour ianswer ias ia ipercent. A) 96.37 B) 49.27 C) 62.61 D) 13.34 E) 72.72 Ans: C 37. Find ithe imean iand imedian iof i . A) mean: 36.00 i median: 36.00 B) mean: 36.00 median: 0.11 i C) mean: 6.00 median: 0.50 D) mean: 9.00 median: 9.00 E) mean: 0.50 median: 0.50 i Ans: D