Normal Distribution
Akshansh Mehta
Questionstats.docx
NOTE: THE CURVES AND AREAS THAT FOLLOW ARE NOT DRAWN TO SCALE
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Problem |
Notes |
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POINT VALUE |
YOUR ANSWER(S) |
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DELETED |
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In figure b-2, if the right tail = 16.6%, how much area (probability) is in the non-tail ? |
4 place decimal Like 0.2563 |
B-2 |
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DELETED |
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In figure b-2, if the large area (probability) = 77.1%, how much area is in the right tail ? |
2 place % |
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DELETED |
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If a z score is found to be 0.78, what is the resulting probability (AREA) TO THE LEFT OF THE Z SCORE ? |
4 place decimal Like 0.7563 |
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If a probability or area is found to be 0.7190, what is the z score ? |
2 place decimal like 0.77 or 1.35 |
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If a probability or area is found to be 0.3399, what is the z score ? |
2 place decimal like 0.77 or - 1.09 |
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If a probability or area is found to be 0.7370, what is the z score ? USE THE FIGURE FOR #7 ABOVE
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2 place decimal like 0.77 or 2.59 |
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If a z score is found to be -2.56 , what is the resulting probability ? USE THE FIGURE FOR #8 |
4 place decimal Like 0.2563
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If a z score is found to be – 1.0 , what is the resulting probability ? |
4 place decimal Like 0.2563
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USE THE FIGURE FOR # 8 |
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If a probability or area is found to be 0.0283, what is the z score ? |
2 place decimal like 0.77
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USE FIGURE FOR #8 |
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If a probability or area is found to be 0.5697, what is the z score ? |
2 place decimal like 0.77
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USE #7 FIGURE |
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PART 2
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Problem |
Notes |
POINT VALUE |
YOUR ANSWER(S) |
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Find the area ( probability ) to the left of a z score of 2.16
Round to 4 decimal places or a % to 2 decimal places |
2.16
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Find the area ( probability ) to the right of a z score of -1.90
Round to 4 decimal places or a % to 2 decimal places - figure not drawn to scale |
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Find the area ( probability ) in a right tail where the z score is 1.59
Round to 4 decimal places or a % to 2 decimal places - draw your own figure if necessary
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Find the area of the shaded region between the z scores
Round to 4 decimal places |
-2.32 1.09 |
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If the area of the shaded region is 31.05% or .3105, find the z score at the question mark.
Round to 2 decimal places |
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Find the z score if the NON-shaded region indicated by the arrow is .0293 Round to 4 decimal places
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When a bell curve is shaded from a z score of ZERO (0) all the way to positive infinity, what is the area (probability) covered ?
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Find the z score if the area of the shaded region is .7172
Round to 2 decimal places
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Find the z score if the area of the shaded region is .0298
Round to 2 decimal places
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PART 3
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10. NOTE: THE ANSWER IS NOT A ZSCORE—IT IS A %
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This is a typical bag of broken pretzels—the pretzels are purposely broken to provide a surface for various flavor coatings. It is found that the average number of pieces (after whole pretzels are broken) is 301.68 pieces with a stdev of 32.8 pieces. If a random bag is selected, find the probability that the bag will contain less than 265 broken pieces.
ROUND TO 2 DECIMAL PLACES |
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11. The answer is a value—not a probability.
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The garbage service truck is known to wake us early in the morning. This company’s truck is almost always on time---the average difference in their times is 13.26 minutes with a stdev = 8.22 minutes. The company requires the crews to be 97.22% efficient—meaning that any time below the 97.22% cutoff will result in a warning for driver and crew. Find the lowest value that will not result in a warning—I am looking for the cutoff score. Round to 2 decimal places.
THIS IS A BELL CURVE CUTOFF SCORE PROBLEM |
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This is a tank less water heater; it has advantages and some disadvantages. Theoretically, a tankless water heater will provide your home with a limitless supply of hot water with next to no warmup time. For this problem, the average tankless takes 7.24 minutes to heat water with a stdev = 1.03 minutes ( depending on several factors). Find the probability that a randomly selected tankless will take BETWEEN 5.98 minutes and 8.09 minutes to heat up.
Leave answer at 2 decimal places.
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5
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13.
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Your parents and/or grandparents may have told you about their old television set ( “we only had 3 channels and the set had to warm-up”). It has been researched and reported that these old tvs took an average of 15.6 seconds to warm up with a stdev= 6.08 seconds. If a sample of 16 old tvs is selected at random, find the probability that it will take MORE than 13.07 seconds to warm up. Answer to 2 decimal places
And we didn’t have remotes either !
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CHAOTER 7 PROBLEMS
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SHARKS |
5 POINTS |
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DOLLS |
5 POINTS |
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Bonus problem: Not covered by the instructor
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Problem |
Notes |
POINT VALUE |
YOUR ANSWER(S) |
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Bonus |
The average size of a rhododendron tree is 19.4 feet; if 20.5% of all rhododendrons are higher than 22.79 feet, find the stdev. Round answer to 2 decimal places.
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4.4329722183837411E-3 4.5677479282173082E-3 4.7061505870534034E-3 4.8482619928781508E-3 4.994165288576484E-3 5.1439449687883942E-3 5.2976868862858574E-3 5.4554782578522228E-3 5.6174076696454628E-3 5.7835650820267171E-3 5.9540418338351365E-3 6.1289306460901001E-3 6.3083256251015209E-3 6.4923222649689869E-3 6.681017449450188E-3 6.8745094531790967E-3 7.0728979422141564E-3 7.2762839738966748E-3 7.4847699959995385E-3 7.6984598451463153E-3 7.9174587444806634E-3 8.1418733005660417E-3 8.3718114994956218E-3 8.6073827021922802E-3 8.8486976388785846E-3 9.0958684026967353E-3 9.349008442458364E-3 9.6082325545042407E-3 9.8736568736539944E-3 1.0145398863225973E-2 1.0423577304107614E-2 1.0708312282856652E-2 1.0999725178813802E-2 1.12979386502076E-2 1.1603076619232386E-2 1.1915264256080461E-2 1.2234627961909888E-2 1.2561295350729454E-2 1.2895395230182726E-2 1.3237057581213355E-2 1.3586413536594176E-2 1.3943595358302769E-2 1.4308736413726953E-2 1.4681971150683489E-2 1.5063435071234213E-2 1.5453264704283926E-2 1.5851597576944862E-2 1.6258572184653212E-2 1.667432796002349E-2 1.7099005240427213E-2 1.7532745234282606E-2 1.7975689986043278E-2 1.8427982339873573E-2 1.8889765901999631E-2 1.9361185001725446E-2 1.9842384651104047E-2 2.0333510503254652E-2 2.0834708809317204E-2 2.1346126374036677E-2 2.1867910509970206E-2 2.2400208990310762E-2 2.2943170000322293E-2 2.3496942087381768E-2 2.4061674109624401E-2 2.4637515183189712E-2 2.5224614628066393E-2 2.5823121912535305E-2 2.6433186596210786E-2 2.7054958271681404E-2 2.7688586504752481E-2 2.8334220773293319E-2 2.8992010404693871E-2 2.966210451193587E-2 3.0344651928285032E-2 3.103980114061216E-2 3.1747700221351489E-2 3.2468496759106673E-2 3.3202337787915169E-2 3.3949369715183614E-2 3.470973824830758E-2 3.5483588319990503E-2 3.627106401227792E-2 3.7072308479324266E-2 3.7887463868910801E-2 3.871667124273459E-2 3. 9560070495489798E-2 4.0417800272763593E-2 4.1289997887770852E-2 4.217679923695266E-2 4.3078338714465023E-2 4.3994749125586076E-2 4.4926161599070799E-2 4.5872705498483705E-2 4.6834508332542164E-2 4.7811695664503016E-2 4.8804391020627703E-2 4.98127157977621E-2 5.0836789170068251E-2 5.1876727994947379E-2 5.2932646718194039E-2 5.4004657278423608E-2 5.5092869010815705E-2 5.6197388550217969E-2 5.7318319733656448E-2 5.8455763502299293E-2 5.9609817802922085E-2 6.0780577488925007E-2 6.1968134220952611E-2 6.3172576367168595E-2 6.439398890323933E-2 6.5632453312080952E-2 6.6888047483426111E-2 6.8160845613267865E-2 6.9450918103239112E-2 7.0758331459987389E-2 7.2083148194605734E-2 7.3425426722181927E-2 7.4785221261528562E-2 7.6162581735158635E-2 7.7557553669571677E-2 7.8970178095915999E-2 8.040049145109511E-2 8.1848525479385301E-2 8.3314307134634086E-2 8.4797858483108585E-2 8.6299196607064727E-2 8.7818333509108615E-2 8.9355276017421686E-2 9.0910025691922663E-2 9.2482578731439308E-2 9.4072925881964226E-2 9.5681052346068385E-2 9.7306937693548173E-2 9.8950555773380286E-2 0.10061187462706082 0.10229085640340403 0.10398745727487736 0.10570162735554864 0.10743331062072252 0.10918244482834263 0.1109489614422355 0.11273278555727408 0.11453383582653609 0.11635202439053419 0.11818725680859427 0.1200394319924571 0.12190844214217882 0.12379417268440623 0.12569650221310005 0.12761530243278105 0.12955043810437211 0.13150176699370855 0.13346913982278941 0.13545240022383945 0.13745138469625329 0.1394659225664899 0.14149583595098583 0.14354093972215429 0.14560104147753572 0.14767594151216404 0.14976543279421253 0.15186930094398032 0.15398732421628011 0.15611927348628626 0.15826491223889941 0.16042399656168455 0.16259627514143465 0.16478148926441311 0.16697937282032432 0.1691896523100605 0.17141204685727124 0.17364626822379944 0.17589202082902522 0.17814900177315826 0.18041690086451537 0.18269540065081824 0.18498417645454457 0.18728289641236248 0.18959122151867597 0.19190880567330687 0.19423529573333562 0.1965703315691211 0.19891354612451628 0.2012645654812952 0.20362300892780183 0.20598848903183059 0.20836061171774403 0.21073897634783123 0.21312317580790668 0.21551279659714695 0.21790741892215976 0.22030661679527538 0.2227099581370503 0.22511700488296596 0.22752731309430613 0.2299404330731907 0.2323559094817417 0.23477328146535398 0.23719208278003931 0.23961184192381071 0.24203208227206885 0.24445232221695098 0.24687207531059793 0.24929085041229343 0.25170815183942447 0.25412347952221065 0.25653632916214558 0.25894619239409095 0.26135255695196025 0.26375490683792757 0.26615272249509053 0.26854548098351727 0.27093265615960199 0.27331371885865019 0.27568813708061374 0.27805537617889109 0.28041489905210609 0.28276616633877621 0.28510863661477615 0.28744176659350373 0.28976501132864846 0.29207782441946262 0.29437965821843237 0.29666996404124241 0.29894819237892567 0.30121379311208901 0.30346621572710086 0.30570490953412532 0.30792932388688676 0.31013890840404457 0.31233311319205648 0.31451138906940795 0.31667318779208181 0.3188179622801412 0.32094516684529717 0.32305425741933103 0.32514469178323985 0.32721592979697045 0.3292674336296 1058 0.33129866798989788 0.33330910035691319 0.33529820121081877 0.33726544426350324 0.33921030668899349 0.34113226935349517 0.34303081704491872 0.34490543870175172 0.34675562764113499 0.34858088178600261 0.35038070389114123 0.35215460176802976 0.35390208850831578 0.35562268270578834 0.35731590867670537 0.35898129667833606 0.36061838312557576 0.36222671080549762 0.36380582908969838 0.36535529414430373 0.36687466913749445 0.36836352444441939 0.36982143784935906 0.37124799474500869 0.3726427883287487 0.37400541979577162 0.37533549852893849 0.37663264228523879 0.37789647737872722 0.37912663885981668 0.38032277069080761 0.38148452591753318 0.38261156683700692 0.38370356516095777 0.38476020217514367 0.38578116889433262 0.38676616621284904 0.38771490505057976 0.38862710649434251 0.38950250193451758 0.39034083319685176 0.39114185266934098 0.39190532342410744 0.39263101933418437 0.39331872518513056 0.39396823678139514 0.3945793610473603 0.3951519161229925 0.39568573145403385 0.3961806478766734 0.39663651769663744 0.39705320476264555 0.39743058453417945 0.39776854414351959 0.39806698245200378 0.39832581010047047 0.39854494955385134 0.39872433513988031 0.39886391308189439 0.39896364152570096 0.3990234905604953 0.39904344223381111 0.39902349056049546 0.3989636415257013 0.39886391308189489 0.39872433513988093 0.39854494955385211 0.39832581010047141 0.39806698245200484 0.39776854414352092 0.3974305845341809 0.39705320476264705 0.39663651769663921 0.39618064787667517 0.39568573145403585 0.39515191612299466 0.39457936104736263 0.39396823678139758 0.39331872518513322 0.39263101933418709 0.39190532342411033 0.39114185266934404 0.39034083319685497 0.38950250193452096 0.38862710649434601 0.38771490505058348 0.38676616621285281 0.38578116889433656 0.38476020217514778 0.38370356516096205 0.38261156683701131 0.38148452591753779 0.38032277069081233 0.37912663885982151 0.37789647737873205 0.37663264228524385 0.37533549852894366 0.37400541979577689 0.37264278832875414 0.37124799474501424 0.36982143784936466 0.36836352444442516 0.36687466913750039 0.36535529414430978 0.3638058290897046 0.36222671080550389 0.3606183831255822 0.3589812966783425 0.35731590867671198 0.355622682705795 0.35390208850832261 0.35215460176803676 0.35038070389114828 0.34858088178600977 0.34675562764114226 0.34490543870175899 0.34303081704492622 0.34113226935350277 0.3392103066890011 0.33726544426351091 0.33529820121082665 0.33330910035692107 0.33129866798990582 0.32926743362961863 0.32721592979697861 0.32514469178324801 0.32305425741933935 0.32094516684530555 0.31881796228014964 0.31667318779209036 0.3145113890694165 0.31233311319206503 0.31013890840405323 0.30792932388689548 0.30570490953413409 0.30346621572710969 0.30121379311209795 0.29894819237893461 0.2966699640412514 0.29437965821844148 0.29207782441947172 0.28976501132865756 0.28744176659351289 0.28510863661478536 0.28276616633878549 0.28041489905211542 0.27805537617890036 0.27568813708062306 0.27331371885865957 0.27093265615961137 0.26854548098352665 0.26615272249509997 0.26375490683793706 0.26135255695196979 0.2 5894619239410044 0.25653632916215507 0.25412347952222014 0.25170815183943401 0.24929085041230295 0.24687207531060745 0.2444523222169605 0.2420320822720784 0.23961184192382029 0.23719208278004889 0.23477328146536355 0.23235590948175125 0.22994043307320022 0.22752731309431568 0.22511700488297548 0.22270995813705982 0.22030661679528488 0.21790741892216919 0.21551279659715644 0.21312317580791612 0.21073897634784067 0.20836061171775341 0.20598848903183994 0.20362300892781118 0.20126456548130453 0.19891354612452555 0.19657033156913029 0.19423529573334486 0.19190880567331603 0.18959122151868513 0.18728289641237159 0.18498417645455362 0.18269540065082726 0.18041690086452436 0.17814900177316723 0.1758920208290341 0.1736462682238083 0.17141204685728004 0.16918965231006927 0.16697937282033301 0.16478148926442177 0.16259627514144323 0.16042399656169307 0.15826491223890796 0.15611927348629467 0.15398732421628852 0.15186930094398868 0.14976543279422083 0.14767594151217225 0.14560104147754391 0.14354093972216242 0.14149583595099388 0.13946592256649787 0.13745138469626123 0.1354524002238473 0.13346913982279718 0.1315017669937163 0.12955043810437977 0.12761530243278871 0.1256965022131076 0.1237941726844137 0.12190844214218623 0.12003943199246445 0.11818725680860158 0.11635202439054143 0.11453383582654324 0.11273278555728121 0.11094896144224252 0.10918244482834956 0.10743331062072942 0.10570162735555544 0.10398745727488409 0.10229085640341072 0.1006118746270674 9.8950555773386822E-2 9.7306937693554627E-2 9.5681052346074782E-2 9.4072925881970554 E-2 9.248257873144558E-2 9.0910025691928839E-2 8.9355276017427793E-2 8.7818333509114652E-2 8.6299196607070694E-2 8.4797858483114469E-2 8.3314307134639914E-2 8.1848525479391074E-2 8.04004914511008E-2 7.8970178095921634E-2 7.7557553669577228E-2 7.6162581735164131E-2 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