What is the purpose of a Z-score in a normal distribution?

To measure how many standard deviations an element is from the mean

To identify the mode of the distribution

To find the median of the distribution

To calculate the probability of an element

If a data point in a normal distribution has a Z-score of -1 , where does it lie in relation to the mean?

It is one standard deviation below the mean

It is two standard deviations below the mean

It is one standard deviation above the mean

What does a Z-score of 0 represent in a normal distribution?

The data point is exactly at the mean

The data point is one standard deviation above the mean

The data point is one standard deviation below the mean

The data point is two standard deviations above the mean

In a normal distribution, what does the area under the curve represent?

The total probability which equals 1

The standard deviation of the data

Z-SCORE AND PROPERTIES OF NORMAL DISTRIBUTION

Normal distribution and its properties, empirical rule, z-score

Generate all of these 25 questions Part A: Each correct answer is worth 5. 1. The regular pentagon shown has a side length of 2 cm. The perimeter of the pentagon is (A) 2 cm (B) 4 cm (C) 6 cm (D) 8 cm (E) 10 cm 2 cm 2. The faces of a cube are labelled with 1, 2, 3, 4, 5, and 6 dots. Three of the faces are shown. What is the total number of dots on the other three faces? (A) 6 (B) 8 (C) 10 (D) 12 (E) 15 3. The equation that best represents \a number increased by _ve equals 15" is (A) n 􀀀 5 = 15 (B) n _ 5 = 15 (C) n + 5 = 15 (D) n + 15 = 5 (E) n _ 5 = 15 4. The line graph shows the number of bobbleheads sold at a store each year. The sale of bobbleheads increased the most between (A) 2016 and 2017 (B) 2017 and 2018 (C) 2018 and 2019 (D) 2019 and 2020 (E) 2020 and 2021 Number of 2016 2017 2018 2019 2020 Year Sale of Bobbleheads 2021 Bobbleheads 20 40 60 80 5. Starting at 72, Aryana counts down by 11s: 72; 61; 50; : : : . What is the last number greater than 0 that Aryana will count? (A) 4 (B) 5 (C) 6 (D) 7 (E) 8 6. In the diagram, \ABC = 90_. The value of x is (A) 68 (B) 23 (C) 56 (D) 28 (E) 26 Day of the Week 44° x° A B C x° 7. Which of the following values is closest to zero? (A) 􀀀1 (B) 5 4 (C) 12 (D) 􀀀4 5 (E) 0:9 Grade 8 8. A jar contains 267 quarters. One quarter is worth $0.25. How many quarters must be added to the jar so that the total value of the quarters is $100.00? (A) 33 (B) 53 (C) 103 (D) 133 (E) 153 9. A package of 8 greeting cards comes with 10 envelopes. Kirra has 7 cards but no envelopes. What is the smallest number of packages that Kirra needs to buy to have more envelopes than cards? (A) 3 (B) 4 (C) 5 (D) 6 (E) 7 10. For the points in the diagram, which statement is true? (A) e > c (B) b < d (C) f > b (D) a < e (E) a > c y x (e, f ) (a, b) (c, d ) Part B: Each correct answer is worth 6. 11. The 26 letters of the English alphabet are listed in an in_nite, repeating loop: ABCDEFGHIJKLMNOPQRSTUVWXY ZABC : : : What is the 258th letter in this sequence? (A) V (B) W (C) X (D) Y (E) Z 12. A public holiday is always celebrated on the third Wednesday of a certain month. In that month, the holiday cannot occur on which of the following days? (A) 16th (B) 22nd (C) 18th (D) 19th (E) 21st 13. A circular spinner is divided into three sections. An arrow is attached to the centre of the spinner. The arrow is spun once. The probability that the arrow stops on the largest section is 50%. The probability it stops on the next largest section is 1 in 3. The probability it stops on the smallest section is (A) 1 4 (B) 2 5 (C) 1 6 (D) 2 7 (E) 3 10 14. A positive number is divisible by both 3 and 4. The tens digit is greater than the ones digit. How many positive two-digit numbers have this property? (A) 4 (B) 5 (C) 6 (D) 7 (E) 8 15. A rectangular pool measures 20 m by 8 m. There is a 1 m wide walkway around the outside of the pool, as shown by the shaded region. The area of the walkway is (A) 56 m2 (B) 60 m2 (C) 29 m2 (D) 52 m2 (E) 50 m2 20 m 8 m 1 m Grade 8 16. The results of asking 50 students if they participate in music or sports are shown in the Venn diagram. What percentage of the 50 students do not participate in music and do not participate in sports? (A) 0% (B) 80% (C) 20% (D) 70% (E) 40% Music Sports 15 5 20 17. There are 2 3 as many golf balls in Bin F as in Bin G. If there are a total of 150 golf balls, how many fewer golf balls are in Bin F than in Bin G? (A) 15 (B) 30 (C) 50 (D) 60 (E) 90 18. In the sequence shown, Figure 1 is formed using 7 squares. Each _gure after Figure 1 has 5 more squares than the previous _gure. What _gure has 2022 squares? (A) Figure 400 (B) Figure 402 (C) Figure 404 (D) Figure 406 (E) Figure 408 Figure 1 Figure 2 Figure 3 19. Mateo's 300 km trip from Edmonton to Calgary passed through Red Deer. Mateo started in Edmonton at 7 a.m. and drove until stopping for a 40 minute break in Red Deer. Mateo arrived in Calgary at 11 a.m. Not including the break, what was his average speed for the trip? (A) 83 km/h (B) 94 km/h (C) 90 km/h (D) 95 km/h (E) 64 km/h 20. Equilateral triangle ABC has sides of length 4. The midpoint of BC is D, and the midpoint of AD is E. The value of EC2 is (A) 7 (B) 6 (C) 6:25 (D) 8 (E) 10 Part C: Each correct answer is worth 8. 21. The positive factors of 6 are 1, 2, 3, and 6. There are two perfect squares less than 100 that have exactly _ve positive factors. What is the sum of these two perfect squares? (A) 177 (B) 80 (C) 145 (D) 52 (E) 97 22. In the list p; q; r; s; t; u; v, each letter represents a positive integer. The sum of the values of each group of three consecutive letters in the list is 35. If q + u = 15, then p + q + r + s + t + u + v is (A) 85 (B) 70 (C) 80 (D) 90 (E) 75 Grade 8 23. The net shown is folded to form a cube. An ant walks from face to face on the cube, visiting each face exactly once. For example, ABCFED and ABCEFD are two possible orders of faces the ant visits. If the ant starts at A, how many possible orders are there? (A) 24 (B) 48 (C) 32 (D) 30 (E) 40 A D B C E F 24. The number 385 is an example of a three-digit number for which one of the digits is the sum of the other two digits. How many numbers between 100 and 999 have this property? (A) 144 (B) 126 (C) 108 (D) 234 (E) 64 25. Student A, Student B, and Student C have been hired to help scientists develop a new avour of juice. There are 4200 samples to test. Each sample either contains blueberry or does not. Each student is asked to taste each sample and report whether or not they think it contains blueberry. Student A reports correctly on exactly 90% of the samples containing blueberry and reports correctly on exactly 88% of the samples that do not contain blueberry. The results for all three students are shown below. Student A Student B Student C Percentage correct on samples 90% 98% (2m)% containing blueberry Percentage correct on samples 88% 86% (4m)% not containing blueberry Student B reports 315 more samples as containing blueberry than Student A. For some positive integers m, the total number of samples that the three students report as containing blueberry is equal to a multiple of 5 between 8000 and 9000. The sum of all such values of m is (A) 45 (B) 36 (C) 24 (D) 27 (E) 29

Eff..rs of ott.-PoFllat i What woLrld hoppen ro our colnrry i, it is ovetsp.pulored? When our counrry is ov€.-populdted, re @ €xp€ri.nce rh€ foll.wirg: Food is our bdsic h@d. Wh€n th€.Cs an ih.re.se ir populdtion it neans thar hore ,@d is iealed. It rheds ho .naJgh food, rrtrple irll srruggle wirh eddr oth€r in ordeLro €!'r- As o l!fllr, lhde rill be o f@d -- , ond ou, now]nert of on ihdiyiduol fron d c..tair - the move$eni o, on individudl our of o cerrain pla.e which help r€duce ihe populotion of th6t fr Arcih€. b.sic ned is w.ra. Wde. shorroge ocu.s when there is on ircreare of hu,nber of p@ple ro be $pptied. rn owr-popur.t d ore.s, woler is rdior€d, Ir rEB rhoi supplies like ti,tWSS ond ,IWSI can'i $pply enoish worer. Do you hdve enough supply of sai.. in your oreo? Aside f.om food alld worer, shelier is olso ohe o, our inportant heeds. As the populoiion ihcre.!e!, building n.w hoLr!€s or rhelt€r is limit.i. To find solulion to this prcbl€n, some goverihent og.ncies dnd orhs non{ov€Ihrehl offi.iofs (N6O) .onvefied sot@ ti.elields, du,np site. dnd nountcirlr inlo flbdivisions dnd relidentiols. Sut whot uould be ths effect o{ coMrtiig .i@fields to .6id€nri6l uits in our food supply? z , 2 Z Z :'", becouse there ore no enough space for prcpex garbage dkposol. ^s o r€sulr, sore peoPle lend to ihrow'their gorbdge onywh.f€. oorbdge baones brc{niry ond rursing ground of iEecrs and onidols ihot @se horm ro pe.ple. Dec.yiry garboge olso produces r,hpleaiant odor ard ehen burn if pmduces pois.nour qds @lled nelhohe As ihe populdtion incr€a3*, the 9d6.9e dso incraes. nris is T't ,,8 T H Wha you de living in on oa-populdi.d pla@, you moy oqaiae halrh prcblerns. Ir is be@@. the woi.r srpply is limit.d ihct will l..d you to poor hygi.ni. hobirs. In plo.4 like rhis, the surrouhdiigs naybe uniidy. o focrorthoi @uld oko cfFe.t your h4l'th. The common oilments rhot yd @uld oc$rire in ovesfDpllar€d ploces ore bEnchil is, o5l hnq. diqrrha and rube.culosis. 7,\ ,\\ \1" 6. Lnck of Herlrh sarvice llosi Pelple in 6n oM-populci€d 6ra 90 ro rubli. heilrh @trtas ond governhent hospirols be6u.e ii prcvides fr@ @Eulrorion oid los @sr rEdicdrions. A3 a ..suli, lh€s€ gow.nnenr dg€rciB b.@ne itud.4$re in mcetiig ihe n eds b..ou!€ df ihsrffici€nr funds. Lock of medicol personnel ,o odmaiisi€I is also s problen in mosr hosptols ev€n rhere or. od.audtc supply of hedicire!. 7_ Do you how wlry rhe crim€ roi€ hexs ih becdur€ fiDre pe.ple o.e fnJrrct€d d@ ro sLffici€.i naE io supp.rr their forniliG. ouf country inclY{ses? If is uh.mploym€ni dnd hdve no arinet .re u$dv gr€{rer ia dn dq-popltdled ra whq. tl, , a, v, tlr I E. Air ard Wat€r Pollutioh How dir be.o'nes pollut€d? I11€ dir b@'n€s p.llurn be.4ne of rhe hormfolgoees thot ser. produ.4 by the fdciori€s and vehicles. Itete {octories ond whi.l6 @ fuel ro run nochiB ond .JBin6. In ,h€ prc.ess, they give our Cdrboh Dioxide ond other ho.6ful gars.r such 6 Nittugei Oxide, Corbon l oioxide dnd Le.d iiio the oir. Do you know whot .ontdbute io ihe incr€asing number of whides qnd foctories? It is ihe inc.6e o, populdtion. As whdt I hove dis.!sse!, wirh a lihired sra.e 9@bd9e disposalie one of the problens thot .o!ld ise i, dh o!er-pop!,.t€d ploce. exn,jple ot thie orc rhos€ pelpl€ livi,rg oh the raverside teid 'ro ,hrou, lheir gEr&ge Hde you seen 'th. P6si9 river or the Tulyahan river? Did you {ind it Whdr do you think i! ihe eff€.t of ihis ih the.re4iures sho lives ih Ahothd f6do.s thal could.on rlbule to wdtd pollutioh dre oil s?ills, gorbqg€ fro,n boa, or ships ahd som€ ihdust.iol wosre. 9. Ite l@96f p4.enroge group. Individuols who orc this grclp. of olr popllarioh is compos.n of the working @pobla of s'rpporting ,heir fomilies nok !-up Though rhas group hol& the lojgeei percenroge of d. populaiion, rhis olso becomer one o{ oveFpopulored probl€]ns b€4use there ore rc jobs awildble fo. oll of iha10. Erergy Shortdge ltere will be on energy shortdge iJ ihe populdtion incre63"l be.dise rhe d.,nand i. €le.iriciry is high. Why is thai wh.n th. PoPqldion inclE.g, rhe d4ord in el4tricity is high? Ir B be.ouse there $,ould be 8to.e hdsat dnd blildirys to lighr ond nore el?riric oPPliohces ro run. rt.6rcznho!3.Ef+ed Whor is rhe grernho@ eff€.r? In whoi say il c.uld offect c2 6re.hhG. effed is rhe wdrniltg of rhe drltlosphee. lvhen the 5un worft rhe.nrrh s1jrf.@, sone of rhe h@r go€J bo.k ro rhe ornos?herc. Air an the dtnDsphere which is C@boi Dioxid. ,rops ihe heot 6hd it mok6 the a.th very worm. As ihe populdtion coniinuou!|,l gtol4 , the gt@rl$use etfe.t b@res no.e visible. Ir is becaosu ,hera ore mo.e focrories snd whicl.s iha, produce wdst€s ond fuma5 which cduses more C{.bo. Diodde ir the ormosphere. As a rcsutt, ,herc eiould be nore h4, ,rop in the ornosphere uhich osk6 th. @ih nuch wornerIf this will hoppen continuously, ,h€ fish ih th€ ocah *ill di€, ricerields/f@mlands will dry too due to lh€ wcm clitnole 12. Destruction of rhe Ozone Loyer A5 whot you hove l@med lrheh you de in v5-6, rhot the qzore ldver is 'the proiecrive loy€. of the olnosPhd€. ft protects us {rom the homful effects of ultrdviolei rays of the su. Do you khow ,hot our Ozore lol€t q4. dQ4tt\!ci.d? Il olreadY hod holes lhai dllow the ulrroviolet rdys to .4dt ihe @rrh. How do6 this hdpPei? Does th. in rc$e of poPuldioh h@€ sonething 'to do tr,lh ir? Yes, rhe I6i grov/irts PoPuldiion .odribuied o lot be@use 6 th' populotion incre3es, rhe u5e of refrigerd'tors, d€rosol lProvs 6nd pl4srics 6bo ihcre&s6. The sid producls coiiojn chemicol called Chlorofluorocdrbons (CFCS) which is mix wafh ihe dir in ihe ormosPher€. As o resulr. ihe hcrmfirl chernicol r€oches the Prolectiw ldver dnd lhrowh. hole in {hid ult@iolzi cahders aid cai4.ct3 ,F.*Y.iis hi!586$q€9.7,- Ho$ doas dcid rdin form? Is cid roii hdmful ro rEn? In the prcvious dis.ussions, yodt€ t.on€d rhd more vel .1e3 dnd fdctori€s or€ necded fo het the iii:.e.siry number o{ P@Pla. Lefs now fihd af hd f@tot.i€s dnd vehicle! .ontribure in the forrEtion of ocid When foctories 6nd whi.ler give off woste gd..3 ,hot will ,nix on lhe noisture i. rhe oir, it will ihen Produ.e sulPhu.i. ocld dnd Nitri. o.id. 'Ihe clol,Jd folb will ,h€h obsorb rhese ccids ond ehei ihe clold f.lls os .oin, ih. ccid is ahady Pdrr of itU/ha d.id ftin falls oh lok"!, ,46 or ocan ih€ fish sill die d.d if h fdlls oh fopnlonds,lhe pldni. together oith the soil B desrroyed. When you inhole dir with Niiric acid, your blood will los. irs @pobilily io fonspori Oxyg€h to your diff€.ai bodY Po.i3. ScieniisB include other rorns oJ dcidic pr€cipiigrion. Thes€ drc nisi, Do you krcw ihot Nuclerr power slotionr Use .adiodctive ,ndie.ials in producirE fuels, yet, rhey do and those .odioactiw rndlqlotE gi\e otf radio'ting en.rgy thoi is harmrul 'to livirq thilEs. wlren rodiotion enlert ihe body ot living things it {ill srq rhere for o lorg ,eriod of ri'ne. Exonple fhe rodiqtion vG srilled to the c.m. Then rhe @rn will be aie by rhe chicken, the .odiotion o the c.rn 'rill also 'tronsf€r to the chi.k€n. Wha on individuol als ihe nat of the chickeh sith mdiarion, helshe rill .ko oblorb ihe rodi@.tirc mtaid that will destrcy hB/her .€lls ond ruket hnn/hd si.r. Over-populoiion .on leld to food shoridg€, wdter shorroqe, housiB probl€ms, qdrbog€ probl€rs, lock of halrh sdi.e. tisa ol clit@ rote, oir ond woi€r pollution, uhanpl6ynat, eiergy 5horr69e, grenhoq3€ efreci, desrruction o( th. ozo@ lat/e?, rci.l roi. olld e.l€d. watta

Z Score Tables

Use the Z-Table to FIND the Z-SCORE!

Z scores, standard normal probabilities, empirical rule

Z Scores

Finding z scores from a normal distribution

Related quizzes

Related quizzes