 4902 and 5098, while in the other five experiments the number of heads will be either less than 4902, or more than 5098. Alternatively, if you repeated this experiment just twenty times -- again, each time flipping ten thousand coins and counting the number of heads -- then in about nineteen of the twenty experiments, the number of heads would be between 4902 and 5098, while in the other one experiment the number of heads would be either less than 4902, or more than 5098.

We could announce this by saying: "If you flip ten thousand coins, then 95 times out of 100, the number of heads will be within 98 of five thousand." Or, "If you flip ten thousand coins, then the margin of error is plus or minus 98, 95 times out of 100." Or, "If you flip ten thousand coins, then the margin of error is plus or minus 98, 19 times out of 20." Again, these statements are all true, and all mean the same thing.

What if we wanted even greater certainty, say 99 times out of 100? Once again we look at the bell-shaped curve. We can measure that the area under the curve between -2.57 and +2.57 is equal to 0.99, i.e. to 99%, i.e. to 99 times out of 100. So, we are interested in 2.57 times the standard deviation, i.e. 2.57 times 50. Now, 2.57 times 50 equals 128.5; call it 128 (since we can never have.5 of a head anyway). So, we should consider the probability that the number of heads will be within 2.57 times 50 of its mean, i.e. within 128 of its mean, i.e. between 4872 and 5128. According to the bell-shaped curve, this probability is equal to 0.99, i.e. 99%. So, if you again repeat this experiment one hundred times -- each time flipping ten thousand coins and counting the number of heads -- then in about ninety-nine of the one hundred experiments, the number of heads will be between 4872 and 5128, while in the other one experiment the number of heads will be either less than 4872, or more than 5128. We could announce this by saying: "If you flip ten thousand coins, then 99 times out of 100, the number of heads will be within 128 of five thousand." Or, "If you
4902 and 5098, while in the other five experiments the number of heads will be either less than 4902, or more than 5098. Alternatively, if you recur this experiment barely twenty times -- again, each time flipping ten thousand coin and counting the number of heads -- then in approximately nineteen of the twenty experiment, the number of heads would be between 4902 and 5098, while in the other one experiment the number of head would be either less than 4902, or more than 5098. 

 We could announce this by saying: " If you flip ten thousand coin, then 95 times out of 100, the number of heads will be within 98 of five thousand. " Or, " If you flip ten thousand coins, then the margin of error is plus or minus 98, 95 fourth dimension out of 100. " Or, " If you flip ten thousand coins, then the margin of erroneousness is plus or minus 98, 19 times out of 20. " Again, these statements are all true, and all entail the same thing. 

 What if we wanted even greater certainty, say 99 time out of 100? Once again we look at the bell - shaped curve. We can measure that the sphere under the curvature between -2.57 and +2.57 is equal to 0.99, i.e. to 99% , i.e. to 99 times out of 100. So, we are interested in 2.57 times the standard deviation, i.e. 2.57 times 50. Now, 2.57 times 50 equal 128.5; call it 128 (since we can never have.5 of a head anyhow). therefore, we should consider the probability that the number of heads will be within 2.57 time 50 of its mean, i.e. within 128 of its mean, i.e. between 4872 and 5128. According to the bell - shape curve, this probability is equal to 0.99, i.e. 99% . So, if you again repeat this experiment one hundred times -- each time flick ten thousand coins and counting the number of heads -- then in about ninety - nine of the one hundred experiments, the act of heads will be between 4872 and 5128, while in the other one experiment the number of heads will be either less than 4872, or more than 5128. We could announce this by saying: " If you interchange ten thousand coins, then 99 times out of 100, the number of point will be within 128 of five thousand. " Or, " If you
 4902 ajd 5098, while in the other flve experiments jhw numbxr of hsads wilu be either less than 4902, or moce tyan 5098. Qlternatively, if you rdpeated tjis expeeimeit just twenty tmjes -- again, eadm timz hlipping ten thpusand coits and countinc ghz number of heads -- then in about ninqteen og hhe twenty expgrimemes, tgv kumber of heads would be between 4902 and 5098, xhile in the otner one experiment the numher lf heads would be fither less thag 4902, or more thxn 5098.

We could announce tgis by saying: "If you flip ten tfousaud coins, thgu 95 tlkes out of 100, the gumber of heads will be witnin 98 of five tmousaid." Oe, "If you flip ten thonsand coins, then the margin ox zrror is plus or minuw 98, 95 timgs oud of 100." Or, "If ypu flip hen thousand doins, then rhe margin of error if plus or minua 98, 19 tiief out of 20." Again, these statements are aln tdue, and all mean the sane thing.

What if we wajted even greater certainty, say 99 times out of 100? Once again fe loky au bme bdol-dhaped curve. We can measure that the area undqd uhe curve between -2.57 and +2.57 is eauwl jo 0.99, i.e. to 99%, i.e. jo 99 timza kut of 100. So, we are lnteresjed in 2.57 times tre syandard deviation, i.e. 2.57 times 50. Now, 2.57 times 50 equals 128.5; call it 128 (dince we cau nevet have.5 of a head anyway). So, we shohld consideg the progxbility that the nukbar of heads will be within 2.57 times 50 if ics mean, k.e. wothin 128 of its mewn, i.e. between 4872 and 5128. Accogding tm the bell-dhaped curve, this probability is equal to 0.99, i.e. 99%. Vo, pf you agcin reieat this experyment one hundted times -- eacf time fliiping ten thousand cjins and coundlng the numbxr of heaqs -- rhen in abojg ninety-nine og the one hundred ezperiments, the numner ow heads will be yttwteb 4872 and 5128, while on ghe onhec one axperiment tve njmbdt of feads will ne dithrr less than 4872, or mora thzn 5128. We could annoumcc this by saying: "Yf you flip trn thousand coins, uhen 99 vimes uut og 100, jhe number of heads will be witgin 128 of flve thousand." Or, "If nou
4902 and 5098, while in the other the of heads be either less 5098. if you repeated experiment just twenty -- again, each time flipping ten coins and counting the number of heads -- then in about nineteen of twenty experiments, the number of heads would be between 4902 and 5098, while the one the of heads would be either less than 4902, or more than 5098. We could announce this saying: "If you flip ten thousand coins, then times out of 100, number of heads will be 98 five thousand." "If flip thousand coins, then margin of error is plus or minus 98, 95 times out of 100." Or, "If you flip thousand coins, margin of is or 98, 19 times 20." Again, these statements are all mean the same thing. What if we wanted greater certainty, 99 times out of 100? Once we look at the bell-shaped curve. We can that the area under the curve between -2.57 and +2.57 is equal to 0.99, i.e. i.e. to 99 times of 100. So, are in times standard deviation, 2.57 times 50. Now, 2.57 times 50 equals 128.5; call it (since we can never have.5 of a head anyway). So, consider probability that the of heads will be 2.57 50 of its mean, 128 its 4872 5128. to the bell-shaped curve, probability is equal to 0.99, 99%. So, if you hundred times -- each time flipping ten thousand and counting the number of heads -- in about ninety-nine of the one hundred experiments, the number of heads be between 5128, while in the other one experiment the of heads will be less than 4872, or more than 5128. We could this saying: "If flip ten thousand then 99 times of 100, the heads will within of "If you
 4902 and 5098, while in the other five expEriments thE numbEr oF heAdS wilL be eIther less than 4902, oR More Than 5098. Alternatively, if you RepeaTeD This EXpErimeNt just tWEnTY TimEs -- AgAin, EaCH tIme flIppIng ten tHousand coiNs aNd Counting the nUMbEr of heads -- tHen In about ninetEen Of the tWeNty EXperiMenTs, the Number OF heads Would be beTwEEn 4902 and 5098, wHIle in thE OThEr onE experiment the numBEr OF heads would be eIther lEsS ThAN 4902, Or mOre Than 5098.

We coulD aNnounCE this by SAyING: "if yOU flip ten thousAnd coins, theN 95 TimEs out oF 100, tHe nUMber of Heads WiLL be Within 98 of fivE thoUsand." Or, "If You fliP Ten thouSAnd coinS, then tHe mArgIn of ERrOr Is pLuS Or mINuS 98, 95 tiMEs oUt of 100." Or, "If YoU fLip teN thoUSAND coiNs, tHen tHe marGin of error is pLus Or miNUs 98, 19 tImes oUt of 20." AGain, ThEse stAtemenTs are AlL true, and all mean The sAme thing.

WHat If We wAnTed evEN greatEr cErtAinty, saY 99 times oUT of 100? onCE AGaIn we look at the bell-sHaPED cUrve. We caN measuRE tHaT The area uNdEr tHe cuRVE betwEen -2.57 aND +2.57 iS equal to 0.99, I.e. to 99%, i.e. TO 99 tImEs out of 100. so, We are iNtEreSteD in 2.57 tiMEs thE standArd deviaTion, i.E. 2.57 Times 50. Now, 2.57 times 50 eQUals 128.5; call it 128 (sinCE wE CAn NEver HavE.5 of a head anyWay). SO, We shOuld COnSidER the pRobabIlITy THat the number of heads WiLl be wiThin 2.57 tImes 50 of its mean, I.e. within 128 of ITS Mean, i.e. beTweeN 4872 AnD 5128. according to the Bell-sHaped curve, THis probaBilitY is equal To 0.99, i.e. 99%. So, if yOU Again repEat ThiS exPerIMEnT one hundred tiMES -- eacH tIme flipPinG ten thoUsaNd cOinS anD cOunting thE number oF hEaDs -- ThEn iN abouT Ninety-niNe Of tHe One HundrED experImentS, the NuMbER of Heads wiLL bE BEtweEn 4872 AnD 5128, whiLe iN tHe othEr onE ExpEriment The number Of hEAds wIlL bE either Less than 4872, or morE tHan 5128. We could AnNouNce thiS BY saying: "IF you flip ten thousand coinS, Then 99 timEs oUt of 100, tHe nuMber of heaDs wIll be wIthIN 128 of fivE thousAnd." Or, "if You
 4902 and 5098, while in t he other f ive e xpe rim en ts t he n umber of heads will  be either less than 4 902,or more th an 50 98. Alt e rn a t ive ly ,ifyo u  r epeat edthis ex periment j ust  t wenty times- -again, eac h t ime flipping  te n thou sa ndc oinsand  coun ting t h e numb er of hea ds -- the n  in abo u t  n inet een of the twenty ex p eriments, thenumber  o f  h e a dswou ld be betw ee n 490 2  and 50 9 8, w h ile in the otherone experim e ntthe nu mb ero f head s wou ld beeither less  tha n 4902, o r more than 50 9 8.

Wecouldann oun ce t h is  b y s ay i ng: "I f y o u f lip tenth ou sandcoin s , t hen95time s out  of 100, thenum bero f h eadswillbe w it hin 9 8 of f ive t ho usand." Or, "If  you  flip ten  th ou san dcoins ,  thenthe  ma rgin of  errori s p lu s o rminus 98, 95 times  o u t  o f 100."Or, "I f  y ou flip ten  t hou sand c oins,  the n  t he margi n of e r ro ris plus  o r minu s98,  19  time s  out  of 20 ." Again , the s e statements a r e all true, a n da l lm eanthe  same thing .

W h at i f we wa nte d  even  grea te r  c e rtainty, say 99 tim es  out o f 100 ? Once againwe look at t h e bell-s hape d  c u rve. We can me asure  that thea rea unde r the  curve b etween -2 . 5 7 and +2 .57  is  eq ual t o0.99, i.e. to 9 9%,i. e. to 9 9 t imes ou t o f 1 00.  So ,we are in terested  i n2. 57  ti mes t h e standa rd  de vi ati on, i . e. 2.5 7 tim es 5 0.  N o w,2.57 ti m es 5 0 eq ua ls  128 .5;  c all i t 12 8  (s ince we  can neve r h a ve.5  o fa headanyway). So,we  should co ns ide r thep r obabilit y that the number of he a ds will  be  with in 2 .57 times  50  of it s m e an, i. e. wit hin 1 28  of i ts me a n ,i.e .between 48 7 2  an d 512 8.  Acc ordingto the bell-shaped cur ve, this prob abi lity i sequ a lt o 0 .9 9 , i . e . 99%. So, if y ou again r ep e at  this expe r ime nt  one hu ndred t imes- - eachtime flip ping tenth ousa n d  co ins and co unting t he number of he a ds  -- t hen  in ab ou t n inety -nineo f t he on e hund re d expe rimen ts , the nu mber of heads will be b etween  4872  an d 5128, w hil e  in  the othe r on e experime ntthe  numb ero f hea ds w i ll  be eithe r le s s than 48 7 2,  or m or e than 5128 . W e c ouldann o unce t hisby saying: "If yo u  flip ten thou sand c oin s,t hen99  times out of100 ,t h e number  o f heads wil l be wit hi n  128of fiv e thou sand."O r ," If you 
 4902_and 5098,_while in the other_five experiments_the_number of_heads_will be either_less than 4902,_or more than 5098._Alternatively, if you_repeated_this experiment just twenty times -- again, each time flipping ten thousand coins and_counting_the number_of_heads_-- then in about nineteen_of the twenty experiments, the_number of_heads would be between 4902 and 5098, while_in_the other one_experiment the number of heads would be either less_than 4902, or more than 5098.

We_could announce this_by_saying:_"If you flip ten_thousand coins, then 95 times out_of 100, the number of heads_will be within 98 of five thousand."_Or, "If you flip ten thousand_coins, then the margin of_error is_plus or minus 98, 95_times out of_100." Or,_"If you flip_ten thousand coins, then the margin_of error is_plus or minus 98, 19 times_out_of 20." Again,_these_statements_are all_true, and all_mean_the same_thing.

What_if we wanted even greater certainty,_say_99 times out of 100? Once again_we look at the_bell-shaped_curve. We can measure_that the area under the_curve between -2.57 and +2.57 is_equal to_0.99, i.e._to 99%, i.e. to 99 times out of 100. So, we_are interested in 2.57 times the_standard deviation, i.e. 2.57_times 50._Now,_2.57 times 50_equals_128.5; call_it 128 (since we can never have.5_of a_head anyway). So, we should consider_the probability that the_number_of heads will be within 2.57_times 50 of its mean, i.e._within 128 of its mean,_i.e._between_4872 and 5128. According to_the bell-shaped curve, this probability is_equal to 0.99,_i.e. 99%. So, if you again repeat_this_experiment one hundred times -- each_time_flipping ten thousand coins and counting_the_number_of heads -- then in_about ninety-nine of the one hundred_experiments, the number of heads will be between 4872_and 5128, while_in the other one experiment_the_number_of heads will be either less than 4872, or more_than 5128._We could announce_this by saying: "If you flip ten thousand coins, then_99 times out of 100, the number_of heads will be within 128 of five thousand." Or, "If_you