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Probability rules. For each of the following situations,

Introduction to the Practice of Statistics: w/CrunchIt/EESEE Access Card | 8th Edition | ISBN: 9781464158933 | Authors: David S. Moore, George P. McCabe, Bruce A. Craig ISBN: 9781464158933 206

Solution for problem 4.20 Chapter 4

Introduction to the Practice of Statistics: w/CrunchIt/EESEE Access Card | 8th Edition

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Introduction to the Practice of Statistics: w/CrunchIt/EESEE Access Card | 8th Edition | ISBN: 9781464158933 | Authors: David S. Moore, George P. McCabe, Bruce A. Craig

Introduction to the Practice of Statistics: w/CrunchIt/EESEE Access Card | 8th Edition

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Problem 4.20

Probability rules. For each of the following situations, state the probability rule or rules that you would use and apply it or them. Write a sentence explaining how the situation illustrates the use of the probability rules. (a) The probability of event A is 0.224. What is the probability that event A does not occur? (b) A coin is tossed three times. The probability of zero heads is 1/8 and the probability of zero tails is 1/8. What is the probability that all three tosses result in the same outcome? (c) Refer to part (b). What is the probability that there is at least one head and at least one tail? (d) The probability of event A is 0.5 and the probability of event B is 0.6. Events A and B are disjoint. Can this happen? (e) Event A is very rare. Its probability is 0.01. Can this happen?

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DietaryFats • Lipids:HDL,LDL,VLDL • Triglycerides:Actualfats • Phospholipids:Cellmembrane • Sterols:Cholesterol,testosterone Primaryenergysourceatrest&duringlow-intensityexercises • Mostconcentratedformofenergy Triglycerides Consistof3fattyacidtailsandoneglycerolhead Comprisesnearly95%offatindiet “triacylglycerol”–technicalterm Usuallycontainsacombinationofdifferentfattyacids Oils–predominantlypoly-andmonounsaturatedfattyacids • Vegetableoils–10-13%saturatedfattyacids • Coconutoil–92%saturatedfattyacids,6%monounsaturated,and2% polyunsaturated FattyAcids Chainsofcarbon&hydrogenwithcarboxylgroup(COOH)atoneend • Lengthvariesfrom4-24carbonbonds Saturatedfattyacids • Containsinglecarbonbond • Fromanimals • Solidatroomtemp Unsaturatedfattyacids • 1ormoredoublebonds • Plantsource • Liquidaroomtempandsolidatcoldtemp Monounsaturated • Onedoublebond Polyunsaturated • Twoormoredoublebonds Weconsumeabout16-18carbonbonds UnsaturatedFormation • Cis–groupsonsamesideofdoublebonds -allowsfattyacidstobend -facilitatesmovementacrosscellmembrane • Trans–groupsonoppositesidesofdoublebonds -producedsyntheticallythough“hydrogenation” TransFat Hydrogenation • Usedincommercialfoodprocessingtomakeliquidoilsmoresolid • Doublebondsonunsaturatedfatbroken,andhydrogenatomsadded • Canbefullorpartialsaturation Polyunsaturated • Doublebondbetweencarbonscountedfromlastcarboninchainfarthest fromcarboxylgroupcarbon • Omega-3,6and9 Omega-3fattyacids Alpha-linoleicacid(ALA) • Essentialfattyacid;cannotbemanufacturedbybody • Ex:soy,canola,andflaxseedoils,leafygreenveggies,fattyfish,andfishoil Eicosapentaenoicacid(EPA) • Marine(oily)fish-(salmon,mackerel,sardines) Docosahexaenoicacid(DHA) • Maincomponentofmembranephospholipase • SamesourcesasEPA Omega-6fattyacids Linoleicacid:notmanufacturedbythebody • Essentialfattyacidinmanyvegetableoils Arachidonicacid-foundinanimals • Precursortoprostaglandins&otherrelatedhormonecompounds Recommendedratio:omega-6:omega-3–4:1 • TypicalWesterndietsare15:1(animalfats) Oleicacid-Omega-9monounsaturatedfattyacid(ex.Oliveoil) • Helpsreducetheriskofheartdiseaseifsubstitutedforsaturatedandtrans fat Sterols&Phospholipids Compriseremaining5%offatsinfoods Sterols-ex:cholesterol,cortisol,vitaminD,andsexhormones • Groupoffatswithfourringstructure • ContainsoneormoreOHgroups&nocarbonyl(=C=O)orcarboxyl(COOH) groups Cholesterol–animalfoods • Cellmembranecomponent Phospholipids • Structuresimilartotriglyceridesbutincludesphosphateinglycerolhead withonly2fattyacids • Structuralcomponentofalllivingtissues Digestionoffats Occursprimarilyinsmallintestine Mixwithbilesalts&digestiveenzymesbeforecrossingintestinalcellmembranes Pancreaticlipase-breaksdownlargefattyacids • Monoglyceridesandfreefattyacids Absorptionoffats Exogenouspathway • Crossintomucosalcellsthroughpassivediffusion • Monoglycerideresynthesizedintotriglycerides Short-(4carbon)&medium-(6-10carbon)absorbedasfreefattyacids • Freefattyacidchainsisboundtoalbumininthebloodstream(non dissolvable) Majorityofdietaryfatsarelong-chainfattyacids Triglycerideincorporatedintochylomicronmolecule • Largetransportmoleculecontainingfats Chylomicroncomposition(lipoprotein) • Triglycerides–92% • Phospholipids–12% • Cholesterol–3% • Proteins–2% Chylomicronsreleasedslowlyintolymphaticvessels&enterbloodstream • Presentinbloodstream–1.5hoursaftermeal • Triglyceridemetabolizedbylipoproteinlipase -fattyacidsandglycerolabsorbedbyadiposeandmuscletissuecells -clearedfrombloodstreamafter12hrfast Chylomicronremnants-formedafterremovaloftriglyceridecore • Takenupbytheliverandremovedfromcirculation Storageoffats Esterification • Fattyacidsreformedintotriglyceridesforstorageinadipocytes • StimulatedbyinsulinandmediatedbyLPL Storedassubcutaneous&visceralfat&intramusculartriglycerides • Ex:myocardialandtypeIskeletalmuscle • Ex:Anhydrous Efficientstorageformofenergy Metabolismoffats Lipolysis-Fatsmobilizedfromstorage&brokendownintoglycerol&fattyacids • Catalyzedbyhormone-sensitivelipase(HSL) • Postabsorptivestate,fasting,starvation,stress,andexercise Fattyacids&glycerolcirculateinblood&takenupbyappropriatetissues • Mostofglyceroltakenupbyliver–metabolizedtoglucoseorreassemble intotriglycerides • Freefattyacids–boundtocarrierproteinandtransportinblood Fattyacidsdistributedtoothertissuesinbodyandmetabolized • Utilizationdependentonnumberofreceptorsites&transportmechanisms incellmembrane • Ex:heartmusclecellshavehighercapacityfatutilizationvs.TypeImuscles fiberwhicharehigherthanTypeII Provideahighsourceofenergybutmetabolicprocesscomplexandslow Metabolismofintracellularfats Fattyacidchainsconvertedtofattyacyl-CoA • Occursinoutermitochondriamembrane Fattyacyl-CoAtranslocatetoinnermitochondrialmatrix • Co-Aremovedandfattyacidattachedtocarnitinemolecule • Re-joinedwithCoAonceinsidemitochondria • Catalyzedbycarnitineacyltransferaseenzymes Increaseduptakeincellswithlargenumberofwell-developedmitochondria Beta-oxidation: • Fattyacidchainsconvertedtoacetyl-CoA&entersKrebscycle • Eachacetyl-CoA–generates10ATP;1NADHandFADHR • Ex:Palmitate-icecarbonfat:8acetylCoAand80ATP Ketones Conversionofacetyl-CoAtoketonebodies • Acetoacetate,acetone,&Β-hydroxybutyrate Upto185gofketonesproduceddailybyliver • Supplies2-6%ofbody’stotalenergyneedsafterovernightfast • Plasmalevels–<0.05MO/L Acceleratedfattyacidoxidation • Increasesproductionofketones • Ketosis Plasmalevels–>0.06MO/L Ketoacidosis–associatedwithdiabeticcomaanddeath Starvation,restrictionofcarbs,impairedmetabolism;Ketonesbecometheprimary sourceofenergyforbrain(76weeks,70%ofenergy) Restrictionofcarbsindiet • Gluconeogenesisoccursinfirst2-3days • After3days,glucoseprimarilymanufacturedfromglycerol Affectonathleticperformance • Lowglycogenstores • Inabilitytosustaintrainingandortrainathighintensities

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Chapter 4, Problem 4.20 is Solved
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Textbook: Introduction to the Practice of Statistics: w/CrunchIt/EESEE Access Card
Edition: 8
Author: David S. Moore, George P. McCabe, Bruce A. Craig
ISBN: 9781464158933

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Probability rules. For each of the following situations,