❖ The Normal Distribution and the 68-95-99.7 Rule ❖

[@martingoold4296]

Doing math with a sharpie? Living life on the edge, bro.

[@benebutterbean2737]

...But it was erasable...a white board thing...

[@danielplantagenet8385]

Bene Butterbean it’s paper I believe!?

[@evhwolfgang2003]

He also used a red dry erase marker It is still un-erasable on the paper! my guess is that he privately noodles out functions on a dry erase board and grabbed a red marker at random for the demonstration.

[@neoistheI]

I think our man here is on the 0.15%?

[@whatthego]

My expensive tuition fee should goes to you, instead of those lazy professor.

[@Alyngiht]

my professor reads the powerpoint and that is it we suppose to figure it out i swear to gawd i hate math

[@jasonli6969]

my professor does not teach this but it will be on the exam !

[@Blahcub]

Keith Chu yeah your English professor isn’t doing you justice

[@Jodylovesyoumostly]

Keith Chu I swear

[@LFSPharaoh]

Blahcub relax..

[@gina72916]

I love it when my KZbin people are crystal clear!

[@noahmcgriff6027]

This video from 10 years ago is still way better then currently text books and teachers, thanks man :)

[@AldosWorldTV]

If patrick is teaching my subject i don't even attend class anymore, been getting me an average of A lol btw fuckin love you man

[@farhanatindick6109]

I can't count how many times you've helped me with my Math dilemmas, Mr. Patrick. I can't thank you enough. But still, THANK YOU!!!

[@kneebarx]

oh my god so simple yet the teachers male it so complex

[@mehdirahan2759]

jeez tell me abt it lol

[@Simmiebird]

Howard Johnson yeah its so easy yet the lecturers make it look hard

[@LFSPharaoh]

I don’t get why everyone makes this stuff so unnecessarily complicated. Even the best KZbin videos on this stuff still don’t make it as clear as it should be. Like I almost want to make my own because I feel I can dumb it down even further. I feel like some things aren’t explained as thoroughly as they should.

[@MsJenniJennJenn]

Thank you. This makes so much more sense now. Your tutorial videos are some of the best I've found.

[@patrickjmt]

Thanks !

[@cindybeadles01]

+MsJenniJennJenn same here!

[@BroomStik123]

+patrickJMT this is really important!! , what would be 6 deviations then? do you know?

[@finalbossd]

+idonthaveaname If you calculate it, 99.9999993% of all data falls within 6 standard deviations of the mean.

[@BroomStik123]

finalbossd lol, seriously. I got 6 deviations on a brain map, I was so damn messed up worst anxiety you could imagine, it was like panic attacks 24/7 non stop but worse. because it never stopped. the anxiety was worse than panic attacks. I had hallucinogenic persisting perception disorder from mushrooms. severee! derealization, depersonalization I could go on.. ohk thanks for info, sorry for ramble haha.

[@mariellerivera3433]

OMG!!!! I UNDERSTAND IT!!! HE EXPLAINED SO DAMN WELL!!!!!

[@natalianjoki377]

ikr!!!

[@tyknz]

Why can't my teacher have just put it like that -.- Thanks, I might pass my exam tomorrow now :)

[@chloedeshong4244]

did u pass it

[@patrickjmt]

you are only looking at one half of the distribution, so you divide by 2

[@patrickjmt]

@dfjndsk2008 thanks, i am going to make a bunch more after the new year : )

[@patrickjmt]

@vplof convert to standard normal and use tables at the end of your stats book

[@patrickjmt]

@jabberwocky685 it is about a foot deep in my little office/room, all around me

[@gandharvakrishna]

I could not believe solving these questions was this easy. Awesome explanation!

[@adrienneabudo8692]

Thank you! I was so lost before this video!

[@rach3895]

Thank you! That was very clear and easy to understand ^^

[@Bobbybbrown1990]

This guy is my go to youtube channel for anything and everything math. Thanks PatrickJMT

[@phumeximba2246]

I have an exam tomorrow and you are VERY helpful!

[@ahmadwilliams2164]

You explained the last 2 weeks of my stats class in about 7 minutes! Thank you! This was very helpful.

[@maitep1810]

best explanation i've seen. thank you!!!!!!!

[@TheGabriel0806]

Thank you! You just helped me past a part I have been stuck on. After your explanation, I'm wondering why I was stuck in the first place. Thanks for keeping it simple!

[@marieedavis2182]

Ding Ding Ding....the bells are ringing...I get it now!! Thank you!!

[@patrickjmt]

@TryLovee you should probably send your tuition to me : )

[@Faraah11]

Thank youu I have been stuck on this lesson for a week now 😅 now I am thinking of watching youtube vids instead of 4 hour class that I don't learn anything

[@charlesspry3286]

what if they ask for a number that isn't exactly one of the standard dev.? for example, if they ask what the prob. is that people have at least 112?

[@alaysias.5269]

Oh my gosh..... I UNDERSTAND IT! YAAAYY!

[@patrickjmt]

+alaysia spruill yaaaaay :)

[@alaysias.5269]

Thank you for helping everyone out with this.

[@patrickjmt]

@bakopala happy to help : )

[@patrickjmt]

@Chaminade14 that's ok too

[@patrickjmt]

@revdj wonderful! i am flattered : ) tell everyone thanks for mentioning me!

[@patrickjmt]

@xstncd no problem!

[@mikeljessica1]

I finally could answer my homework problem! Thank you so much.

[@patriotdogdad3118]

Q brought me here.

[@crashfan9997]

What?? Q from James Bond?

[@patrickjmt]

@SabaskaTheNoob yep

[@patrickjmt]

@2HanChan3 glad i could help :)

[@milkteaful]

Thanks! This was a good quick review before my test for stats :)

[@NiyaIyana]

Thank u so much, bcuz while in class I couldn't understand that rule to save my life

[@bryceriley2880]

Your video on normal distribution was what I needed. Thank you, it was not making any sense to me.

[@hundetrainer-ammersee]

Great! Finally I got it ... Thank you very much!

[@patrickjmt]

@MixTheMeister thanks! : )

[@Iwantblueberry]

You Sir are the fucking Man!

[@patrickjmt]

you are very welcome :)

[@farwanqv]

I understood the concept overall. But I am still confuse that why do we always divide a normal distribution in 3 parts on both side no matter whatever SD is i.e if SD was 6 then we would have +/- 6 to the mean to find points within 1 SD? Also can someone give examples where SD is not divided into exactly 3 parts?

[@quaresma7besiktas13]

i find it boring to listen to my teacher İn the lesson so youtube teachers like you help me pass the course THANK YOU! :)

[@biaoliant]

Thank you so much!!! Very helpful!

[@mseharrris]

Excellent explanation! Now if the question was: What percentage had an IQ between 115 and 55? How would you go about solving that?

[@gomerpyle6113]

I don't think you can because of the low outliers, but hopefulyl someone else will answer

[@finlaywelford4339]

Set X~N(100,15^2) and solve P(55 ≤ X ≤ 115). Normalise using Z = (X - µ)/σ, i.e. the problem becomes P(-3 ≤ Z ≤ 1), and look up values in normal tables, calculating Φ(1) - Φ(-3) = .8413 - .0013 ≈ 84%

[@allanochoa4826]

you are a big help man!!! thank you :D

[@rilindgashi931]

analizat e gjakut

[@davidmonroy7550]

Who else in AP Statistics 🙃

[@franlee7651]

You are amazing! haven't seen anyone with this much passion and dedication!

[@katecastel7682]

thank you so much this help me a lot!!!

[@patrickjmt]

happy to help

[@patrickjmt]

beats me

[@poldek1337]

How many standard deviation units fall within a normal curve?

[@mahoganyduvall23]

I see what you are doing... but im still a bit confuse on question three when I calculated it 68 divided by 2 is 34 and 34 divided by 2 is 17

[@IceyJunior]

why is it 68% ? how do you prove it ?

[@perilousgourd360]

This happens to be where the FWHM (full width at half maximum) lies for the normal distribution. That is, at one standard deviation greater than the mean, and one standard deviation less than the mean, the height of the normal distribution function has fallen to half of its maximum value. As far as I know, the decision to use FWHM to define the standard deviation was arbitrary, beyond being simply convenient.

[@goatmilk9857]

Wow! This is very helpful, thank you!

[@nadapandaeats]

Thank you!

[@Somalidoc321]

Didn’t think I’d be back 5 years later to watch another video this time to study for USMLE step 1! You’re the GOAT

[@sherlockholmeslives.1605]

My Mensa IQ scores were over 1 standard deviation above the mean average.

[@michellematthews773]

This is fantastic thank you!

[@gooddeedsleadto7499]

For 4.5 standard deviations away from mean, how to find the chance of occurrence? The answer is 6.8 out 1 million for two tails. Thanks for your reply Best Regards Given: Lower Specification limit = 97 mm Higher specification limit = 103 mm I want chance of an event happening out of the the boundary to be, 2 out of a billion, This means 103 mm & 97 mm are 6 standard deviation away from the mean, μ=100 mm. This means σ = 0.5 mm Because (100-97)/ 6 = 0.5 mm

[@devondevon4366]

Assuming this can be measured , what if we are comparing Population B with 115 mean vs Population A with 100 mean and Mensa required at least a 150 mean, then since 150 is GREATER THAN Population A, three standard deviation. (145 or 100 +45) therefore less than 0.15%(using the 99.7 and dividing 0.30 by 2) of Population A would score 150 and above (Actually it is around .05%). However, since 150 is LESS THAN Population B three standard deviation. (160 or 115+45) therefore more than 0.15% of Population B would score at least 150 or more (Actually it is around 1%). So Population B would have a 1/0.5 or 20 .0 advantage . In other words, for every 1 million people Population B has , Population A would need 20 million people to have the same number of people in Mensa (requiring a minimum of 150 to be admitted).

[@Kurtlane]

Thanks, Patrick. It's very clear. One question, though. The standard deviation of 15 - is that "the rule," or just the data for this specific problem? Another question. I am looking for proof of the normal distribution formula Phi(x) = 1/sqrt(2pi*sigma^2) * e^(-(x-mu)^2/2sigma^2) Do you know where I can find it? Also, who figured out this is the standard distribution formula? Any book you can recommend. Thanks

[@devondevon4366]

Assuming that this can be measured (and it is distributed this way), so 100=100, as 'both' are at the mean or ( 0 standard deviation from the mean) 115=85 (as both are 1 standard deviation from the mean ) 130= 70 as both are two standard deviation from the mean ,all in the opposite direction). So if comparing , for example, population A with 100 mean vs population B with 115 mean ( all made up ), it would be in population A interest to be more populous than population B, since , for example, say Mensa requires at least 115 to be admitted, then population B would have just a 50/16 or 3.125 advantage, but if Mensa requires at least a 130, then population B would have a 16/2.5 or 6.4 advantage, and if Mensa requires a minimum of 145 to be admitted then population B advantage would get larger 2.5/.15 or 16.66 or for every 1 million people population B has, population A would need 16.66 million people to have the same number of people in Mensa that requires at least a 145 to be admitted. But when Mensa required a minimum of just 115, population A only need 3.125 million people to match population B. And if Mensa requires even lower, 100 to be admitted, then population B advantage will even drop further 84/50 =1.68 that is for every 1 million people population B has, population A would need just 1.68 million

[@Tina-op7rm]

Well done! I'd like this more than once if I could!!

[@elleno3365]

What about two-tailed assessments, or more complex questions that cannot be simply divided on the normal curve? For example, the question I am trying to answer: You are evaluating a normally distributed variable that has a mean of 868 and a standard deviation of 420. What total proportion of the data falls below an observation of 507 and above an observation of 1292? Round your answer to 4 decimal places

[@OpenMindedForever]

Wrong, LOL. The answer for, How many 145 is ... 0.135 of u ... using 99.73 precise versus 99.7, LOL

[@woodifwecouldboyarsky9778]

I'm taking statistics right now and I'm stuck on figuring out a 3 part question regarding the 68-95-99.7 rule. I understand up until I have a range to figure out. My question is asking the percentage of scores between 50 and 125. The mean is 100 with a standard deviation of 25. I just don't understand the steps to get the answer to this one.

[@greenbongos]

The first example is one that infuriates me the most. Every time I input 50% it is always wrong, it is usually 47.5 or 49.7, and I have yet to find a KZbin video that shows the difficult side of this math instead of the easy garbage everyone posts videos about.

[@adbasdbasdkasdja7246]

if we calculate it by usin chebychev then result is 1-/1/9 = %89 100-89 = 11, 11/2 to find just +145 = %5.5 why they are so different

[@aaliyahyasameen]

The average score on a standardized test is 500 points with a standard deviation of 50 points. What is the probability that a student scores more than 400 on the standardized test? 98% 82% 16% 2%

[@juanitcolombia]

Great JOB!!! totally helped me ace my test!!!!

[@ShavHD]

how are u learning this in college? im in high school and learning this... haha or do u just go over it again in a more complex way in college?

[@GoodDeedsLeadTo]

Hi Patrick: Could you show standard Deviation (six sigma) application to quality management, where they use DMAIC methodology (Define, measure, Analyze, Improve, Control) to reduce variability or defects? How can they use the formula 1 sigma is abs (pessimistic- optimistic value) /6 for one standard deviation.

[@TryLovee]

Oh my gosh you are amazing! I pay my professor in college hundreds of dollars for him to teach me this stuff and it makes no sense, I log and here and watch this and instantly understand in 8 minutes. Something is not right with this equation...thank you so much (:

[@GoodDeedsLeadTo]

What is better quality in your view? 3 standard deviation or 1 standard deviation? You are accepting lower IQ's with 3 standards deviations than 1 standard deviation, but you are accepting a larger population with 3 standard deviation form the mean than one standard deviation.

[@ggpolanco]

YOU'RE A LIFE SAVER MY MAN

[@johnbennion2114]

Teacher was absent from class and left a confusing power point. Should have given a link to this video. Thank you SO much!

[@nelliezucker7782]

This is the only place I could find a good explanation about how to find second standard deviation. Thank you!

[@revdj]

I assign videos for an online course. They have online homework discussion groups, where they talk about homework and stuff. This week, most of the postings were not about homework, but about how helpful this video was. I thought you should know. DJS

[@thevillaiop7703]

Your illustration and explanation were very helpful in understanding the concept. Thank you so much!

[@sangitasingh8762]

Sir I have I doubt if x is 4 and the distribution is 2,3,4,5,6 what will the squared deviation from x

[@Ipsrc]

when you say 'mean, mew' the letter you use, is that the symbol for mean? i have also seen it written with i think.. x and a line horizontal on top? are they both symbols of identifying the term 'mean'? thank you

[@DavidJonathanMello]

WHY DID YOU DIVIDE THE 0.3 PERCENT BY 2??? You didn't explain why! :(

[@KlaudsG]

You are a life saver, this is the only explanation I have been able to understand. Thank you so much.

[@metallica929]

If only all it teachers made it nice and simple like you do... Patrick for president!

[@Titan13213]

thank you soooooo much i actually understand you unlike my indian math teacher ahha

[@QIrons]

The examples, 85 and 145, were on standard deviations, but how do we determine the percentage above or below a number that does not fall on a standard deviation, like say 93 or something?

[@SabaskaTheNoob]

would they ever ask you to find a value that is not equal to a standard deviation(s) from the mean? e.g., find population with less than 90% (with the standard deviation being 15%).

[@truthsings7]

Thank you ^¬^ it feels lots more simple now that I get it, ha ✔

[@tuanlong9238]

after watching this video twice, I understand the normal distribution, thanks =))))

[@ladyblue1729]

Very helpful. I had to figure out one thing you didn't mention but once I did, it clicked and I got it. Thank you!😃

[@whatsupwithtorii]

Thankx you ! 💖 When I pass this Quiz know your the reason why!

[@LivvyLooification]

because the 32% is accounted for on both sides of the curve (below 85 and above 115). in order to find percentage of values below 85, it is half of the 32%

[@xstncd]

LOL OMG, my luck! This is EXACTLY what I need help with and its the newest vid especially since I am stuck with this. ps. my teacher sucks >>". THANKS PAT!

[@saikumar802]

Ur at ur best in this video ...tq so much for sharing ur knowledge with us........ :-)

[@saikumar802]

Ur at ur best in this video ...tq so much for sharing ur knowledge with us........ :-)

[@ashb1597]

i wanted to thank you for a long time but I had not opened a gmail account. But I am ...and thank you so much..you have been a great help for a while...

[@purplebug21]

LOL, i was about to subscribe to ur videos bc they really helped me improve my math grades, and i realized i was already subscribed :D UR AWESOME.

[@peychinhwee]

your video help me to revise my math after 10 years from college, I use to score A for math, but long time never practice it, you lose it. Good video.

[@Chadwickyboy]

What is the link between the # of SDs and tge percentage? In other words, why is 68% linked to one standard deviation?

[@MrAaronsrun]

This video is very useful even if you know the z-score method. I will definitely use the 68-95-99.7 method to check my work. Thanks Patrick.