Standardizing Normally Distributed Random Variables

I discuss standardizing normally distributed random variables (turning variables with a normal distribution into something that has a standard normal distribution). I work through an example of a probability calculation, and an example of finding a percentile of the distribution. It is assumed that you can find values from the standard normal distribution, using either a table or a computer.
The mean and variance of adult female heights in the US is estimated from data found in a National Health Statistics Report:
McDowell MA, Fryar CD, Ogden CL, Flegal KM. Anthropometric reference data for children and adults: United States, 2003-2006. National health statistics re- ports; no 10. Hyattsville, MD: National Center for Health Statistics. 2008.
For those using R, here is the R code for the examples used in this video:
American female heights example (approximately normally distributed with a mean of 162.2 and a standard deviation of 6.8).
Finding the probability that a randomly selected female is taller than 170.5 cm.
Easiest way:
1-pnorm(170.5,162.2,6.8)
[1] 0.111121
Standardizing route:
1-pnorm((170.5-162.2)/6.8,0,1)
[1] 0.111121
The default in R's pnorm is the standard normal distribution (mean=0, SD=1), so the mean and SD can be left out when dealing with the standard normal.
1-pnorm((170.5-162.2)/6.8)
[1] 0.111121
Finding the probability that a randomly selected female has a height between 150.5 and 170.5.
Easiest way:
pnorm(170.5,162.2,6.8)-pnorm(150.5,162.2,6.8)
[1] 0.8462162
Standardizing route:
pnorm((170.5-162.2)/6.8)-pnorm((150.5-162.2)/6.8)
[1] 0.8462162
10th percentile of heights of adult American females.
Easiest:
qnorm(.1,162.2,6.8)
[1] 153.4854
Alternatively, via the standard normal distribution:
qnorm(.1)
[1] -1.281552
That's the 10th percentile of the standard normal distribution. Converting to the distribution of heights,
-1.281552*6.8+162.2
[1] 153.4854

Пікірлер: 226

  • @kingofgirth8609
    @kingofgirth86097 жыл бұрын

    Videos like these.. 4 years old and still saving the lives of students around the world. Good shit.

  • @jbstatistics

    @jbstatistics

    6 жыл бұрын

    Thanks for the compliment! I tried to make them stand the test of time (e.g. examples that play well through time, no Justin Bieber or Rebecca Black references :).

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    @prernarawat4322

    5 жыл бұрын

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    4 жыл бұрын

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    @ejaazzz

    3 жыл бұрын

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    @davinchow15364 жыл бұрын

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    @mahelapriyadarshana4196

    Жыл бұрын

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    @MORamalho8 жыл бұрын

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  • @jbstatistics

    @jbstatistics

    8 жыл бұрын

    +Marlom Oliveira Thanks Marlom! I'm very glad I can be of help. All the best.

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    @jorgeh1338 жыл бұрын

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  • @jbstatistics

    @jbstatistics

    8 жыл бұрын

    +Jorge Hurtado You're very welcome Jorge!

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    @Anita-cc2sc Жыл бұрын

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    @j.o.s.h.o2 жыл бұрын

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    @AhmedKhaled949 жыл бұрын

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  • @jbstatistics

    @jbstatistics

    7 жыл бұрын

    You are very welcome Amy!

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  • @jbstatistics

    @jbstatistics

    7 жыл бұрын

    You are very welcome Adam. All the best!

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    @georgiteofilov12203 ай бұрын

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    @valsant72268 жыл бұрын

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  • @jbstatistics

    @jbstatistics

    8 жыл бұрын

    +Valeria Santoyo I'm glad I could help!

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    @ICOD739 жыл бұрын

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    @vegeta94x10 жыл бұрын

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  • @shashwatranjanchaurasia976
    @shashwatranjanchaurasia9768 жыл бұрын

    Thanks! nicely explained and really helpful .

  • @iceman9285
    @iceman92859 жыл бұрын

    Really amazing video.Thanks a lot!

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    @Brolnox10 жыл бұрын

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  • @jbstatistics

    @jbstatistics

    10 жыл бұрын

    You are welcome Brolnox.

  • @0xNoemix0
    @0xNoemix05 жыл бұрын

    amazing, thank you so much. so easy with this explanation. you deserve an award.

  • @jbstatistics

    @jbstatistics

    5 жыл бұрын

    Thanks for the very kind words!

  • @Admiralgrusbil
    @Admiralgrusbil3 жыл бұрын

    This is a great explaination!

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    @sultansalam3 жыл бұрын

    Still relevant. Love this!

  • @Gaboaoki97
    @Gaboaoki974 жыл бұрын

    VERY WELL EXPLAINED, THANK YOU

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    @pris36756 жыл бұрын

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  • @jbstatistics

    @jbstatistics

    6 жыл бұрын

    You are very welcome. I'm glad to be of help!

  • @intellectualimage
    @intellectualimage6 жыл бұрын

    thank you for all of your videos

  • @jbstatistics

    @jbstatistics

    6 жыл бұрын

    You are very welcome!

  • @NeonRay
    @NeonRay8 жыл бұрын

    Thank you for this!

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    @hashmarker49943 жыл бұрын

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    @onurucar11123 жыл бұрын

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    @ejaazzz3 жыл бұрын

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  • @JamesIsTheRealKing
    @JamesIsTheRealKing7 жыл бұрын

    Perfect pace, good stuff!

  • @jbstatistics

    @jbstatistics

    7 жыл бұрын

    Thanks!

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    @nikitask96346 жыл бұрын

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  • @mehdichakir3611
    @mehdichakir36119 жыл бұрын

    you can't imagine how helpful your videos have been ! thank you

  • @jbstatistics

    @jbstatistics

    9 жыл бұрын

    You are very welcome!

  • @Akshay-lj4fh
    @Akshay-lj4fh6 жыл бұрын

    Superb video...!!! Very useful!! Thank you.

  • @jbstatistics

    @jbstatistics

    6 жыл бұрын

    You are very welcome!

  • @davidhe7935
    @davidhe79358 жыл бұрын

    Very well explained and clear, well done.

  • @jbstatistics

    @jbstatistics

    8 жыл бұрын

    Thanks!

  • @newbie1590
    @newbie15902 жыл бұрын

    You make it so simple....thank you so much 🤩👍

  • @jbstatistics

    @jbstatistics

    2 жыл бұрын

    You are very welcome!

  • @AmazingWorld-jt8ny
    @AmazingWorld-jt8ny3 жыл бұрын

    Thank you so much !

  • @Jdonovanford
    @Jdonovanford10 жыл бұрын

    Could you explain why in statistical inference one should never standardize a variable according to a sample distribution of the same data and why that would be circular reasoning?

  • @MrColdShiverJr
    @MrColdShiverJr6 жыл бұрын

    What i was looking for. Thanks

  • @jbstatistics

    @jbstatistics

    6 жыл бұрын

    You are very welcome!

  • @meema98
    @meema987 жыл бұрын

    hi can u please explain the difference between central and non central chi square distribution..I want to know the mean and variance for each of them..

  • @marvinharrouldapagkho7703
    @marvinharrouldapagkho77038 жыл бұрын

    thanks this helps me a lot.

  • @varshahushare6981
    @varshahushare69815 жыл бұрын

    Great explanation

  • @anandchitchat6411
    @anandchitchat64118 жыл бұрын

    Thanks for useful video and if possible please make video for Random Process. Thanks again.

  • @juliuscastro9438
    @juliuscastro94386 жыл бұрын

    Best stats videos on KZread

  • @jbstatistics

    @jbstatistics

    5 жыл бұрын

    Thanks!

  • @RedRiverChannel
    @RedRiverChannel7 жыл бұрын

    When I look at 1.22 in the table, I find 0.8888 and NOT 0.111. What is wrong?

  • @jbstatistics

    @jbstatistics

    7 жыл бұрын

    Your table is giving you the area to the left of the value of z. In my example, I needed to find the area to the right. Since the area under the entire curve is 1, the area to the right of 1.22 is 1-0.8888 = 0.1112.

  • @RedRiverChannel

    @RedRiverChannel

    7 жыл бұрын

    ok, thank you!

  • @wiiliskaako5875

    @wiiliskaako5875

    6 жыл бұрын

    you then subtract 1

  • @ivanmanhique7975
    @ivanmanhique7975 Жыл бұрын

    Could you or someone explain me with more details how to find the probability when there are two values like (a

  • @icy-spoon85
    @icy-spoon855 жыл бұрын

    Standardizing is something I'm running into a lot lately, and I'm curious about something. If I have a variable x and I want to identify outliers, I could standardize and remove anything above +/- 1.96, or whichever cutoff I choose. I wonder, if x is not normally distributed (e.g. are quite skewed), are z-scores no longer valid? I think that because z-scores are calculated using the mean, but since x is not normal, the mean is no longer a reasonable value for this. Is this correct?

  • @jbstatistics
    @jbstatistics10 жыл бұрын

    I'm glad you find my videos helpful. The random variable X has a mean of mu (E(X) = mu). (X-mu) is itself a random variable, with a mean of 0. E(X-mu) = E(X) - E(mu) = mu - mu = 0. As a simple example, suppose we have a distribution with a mean of 3. If we create a new distribution by subtracting 3 from every possible value, then the mean of the new distribution would be 0.

  • @cogitateandabet

    @cogitateandabet

    4 жыл бұрын

    that's what i needed...thanks man

  • @adityashikhar6143

    @adityashikhar6143

    3 жыл бұрын

    @@cogitateandabet Man I didn't get it. Can you please explain

  • @eeltauy
    @eeltauy6 жыл бұрын

    Great stuff! I never thought I would ever be interested in probibility and statistics (having had a subpar education in the field), but apparently I was wrong!

  • @jbstatistics

    @jbstatistics

    6 жыл бұрын

    That's good to hear! And trust me, there are more interesting things in probability and statistics than standardizing normally distributed random variables!

  • @eeltauy

    @eeltauy

    6 жыл бұрын

    I'm hooked!

  • @chilledstudentvloggr4732
    @chilledstudentvloggr47327 жыл бұрын

    How do you find the area between -1.72 and 1.22 without using any software computations? or is there a formula for it?:-o

  • @jbstatistics

    @jbstatistics

    7 жыл бұрын

    There isn't a formula -- the area is obtained by numerical integration. If you don't have access to software that will find the area (e.g. R, SAS, Excel), then you would need to look up the relevant values in the standard normal table and make the appropriate calculation.

  • @chilledstudentvloggr4732

    @chilledstudentvloggr4732

    7 жыл бұрын

    Is this by using the (+ and -) zscore table? And thank you for responding! Your videos helped me a lot!

  • @jbstatistics

    @jbstatistics

    7 жыл бұрын

    Yes, you'd use areas from the Z table to find the appropriate area.

  • @rkb6988
    @rkb69887 жыл бұрын

    sir plz help me to solve this... ** Given a normal distribution with a mean of 60 and sd of 14, n=100 what percentage of cases will lie between the score of50 and 65??

  • @praisethankgivingworshipsongs
    @praisethankgivingworshipsongs8 жыл бұрын

    Thank you.

  • @aditipant46
    @aditipant467 жыл бұрын

    Thanks, this really helps!

  • @jbstatistics

    @jbstatistics

    7 жыл бұрын

    You are very welcome.

  • @stucatz1130
    @stucatz11308 жыл бұрын

    Great videos, thank you for taking the time upload these lessons! How did you find the Z value for the 10th percentile on this distribution curve? I am familiar finding the value of the 10th percentile (using norminv fx in excel) but not sure how you derived Z score of 10th percentile I look forward to your response,

  • @jbstatistics

    @jbstatistics

    8 жыл бұрын

    +promar In the video I needed to find the 10th percentile of the standard normal distribution. This can be found using software, or a standard normal table if software is not available. I used the R command qnorm(.1,0,1) to find it. I know little of Excel, but the NORMINV command would perform the same function. NORMINV(0.1,0,1) would result in the correct value of -1.281552.

  • @andrewagita901
    @andrewagita9014 жыл бұрын

    god bless u for making these

  • @achievementcell4631
    @achievementcell46315 жыл бұрын

    1. I watched your videos on how to read standard tables but still can not understand how the area got to be 0.111. I think we should look at the table with positive numbers and that gives an area of 0.8888. The table with negative numbers gives an area of 0.111, as you said in the video, but I do not see why we should look at that table in the first place. 2. In the percentiles section, you have marked 0.1 on the left side of our graph. Left side is for negative values, right? Why should 0.1 not come to the right side? I would be glad if you could help me. Great video. Thank you.

  • @abdulbasitraza6204

    @abdulbasitraza6204

    5 жыл бұрын

    we have to subtract the .8888 from 1 in order to have the area greater than z=1.22 and that becomes equal to .111

  • @shefalisingh4675
    @shefalisingh46752 жыл бұрын

    Hey!!! Can u suggest some websites to practice questions based on these concepts? Help appreciated

  • @Jonathanlh951
    @Jonathanlh9519 жыл бұрын

    Can someone explain why the 10th percentile is a value that has an area 10% to the left. Why not the right?

  • @BonyS3k

    @BonyS3k

    8 жыл бұрын

    +Jono Hermes in this example it means, that you are taller, than 10% of people.

  • @paulwary

    @paulwary

    7 жыл бұрын

    The equivalent situation on the right side would be the 90th percentile, ie a height that is taller than 90% of the population. 100% is the area under the entire curve.

  • @muralithatholu5819
    @muralithatholu58196 жыл бұрын

    simply superb

  • @jbstatistics

    @jbstatistics

    5 жыл бұрын

    Thanks!

  • @leungwallace8552
    @leungwallace8552 Жыл бұрын

    Thank you

  • @govindbhagat7197
    @govindbhagat71976 жыл бұрын

    Simply Great

  • @jbstatistics

    @jbstatistics

    5 жыл бұрын

    Thanks!

  • @rivoobagchi5245
    @rivoobagchi52454 жыл бұрын

    thank you so much

  • @kilsat5030
    @kilsat50303 жыл бұрын

    Good Video

  • @neilrayno5437
    @neilrayno543711 жыл бұрын

    in what video did you compute for the area?

  • @karimkhan1312
    @karimkhan13128 жыл бұрын

    EACH LECTURE IS SHORT AND VERY VERY EXCELLENT -LANGUAGE IS VERY CLEAR - EXCELLENT THANK U AMARJIT ADVOCATE DELHI HIGH COURT INDIA

  • @jbstatistics

    @jbstatistics

    8 жыл бұрын

    +Amarjeet Singh You are very welcome!

  • @rwebo4955
    @rwebo49558 жыл бұрын

    Hello JB statistics. I really like your videos they are so simple to follow and understand with appropriate examples. Please, could you do a video for a transformation of random variables and also Convergence of Random variables.. i tried to find something to learn on this but i couldn't. Or else if its already available please give the name or link so that i can check it out. Stay blessed, your videos are life saver trust me.

  • @jbstatistics

    @jbstatistics

    8 жыл бұрын

    +Alan Lwanga Hi Alan. Thanks for the compliment, and I'm glad to be of help. I doubt that I'll have time in the near future to make videos on those topics. I'm sure there are some good resources out there, but I don't have any suggestions. All the best.

  • @vitorbarros8969
    @vitorbarros89693 жыл бұрын

    you're the best bro

  • @charlottemkhize
    @charlottemkhize6 жыл бұрын

    the last question really confused me i do not understand where we got the z= -1,28 from and dat was the reason i watched this video can someone please explain @jbstatistics

  • @jbstatistics

    @jbstatistics

    6 жыл бұрын

    -1.28 is the 10th percentile of the standard normal distribution, and it can be found using software or a standard normal table. If you don't know how to use the standard normal table, then it would be helpful to watch one of my videos on using the standard normal table (e.g. kzread.info/dash/bejne/X4mgzKucocLYlsY.html).

  • @charlottemkhize

    @charlottemkhize

    6 жыл бұрын

    jbstatistics thank you so much Sir, I have a statistic exam tomorrow and your quick response has helped me a lot thank you thank you and I do get it now ☺

  • @seerat1000
    @seerat10008 жыл бұрын

    hi, you are great at explaining sir. I have question . I look at the value 1.22 on the table it have the probability 0.8888 and -1.22 had probability of 0.1112 . if the standard deviation is 1.22 how come the prob is 0.1111 ? thanks

  • @bhagirathtallapragada4699

    @bhagirathtallapragada4699

    8 жыл бұрын

    +Seerat Raseen Yes apparently the negative value has been mistaken for the positive one! had the same doubt.

  • @jbstatistics

    @jbstatistics

    8 жыл бұрын

    +Bhagirath Tallapragada The question is asking for the probability that a randomly selected female is *taller* than 170.5 cm. So we need the area to the *right* of 170.5 under the appropriate normal curve. This is equal to the area to the *right* of the calculated z-score (1.22) under the standard normal curve. When you run off to the z table and look up 1.22, the table gives the area to the *left*, which is not what we need. The standard normal distribution is symmetric about 0, so the area to the *right* of 1.22 is equal to the area to the *left* of -1.22. This is why when you look up -1.22 in the table, you find the final answer. You can also find the final answer by subtracting the area to the left of 1.22 from 1.

  • @shpresajahja6794
    @shpresajahja67947 жыл бұрын

    i have a problem can you help me about this exersise N(32 , 2 ) P(27

  • @mohitpuri3045

    @mohitpuri3045

    7 жыл бұрын

    solve copying procedure as he did

  • @mobilbear

    @mobilbear

    7 жыл бұрын

    for your first case, μ==E=32, σ=Var=2, then your Z1=(27-32)/2=-2.5, your Z2=(29-32)/2=-1.5. So problem now is P(-2.5

  • @mhdalkadri9228
    @mhdalkadri92287 жыл бұрын

    Man you are amazing. you should teach in my University !!!

  • @jbstatistics

    @jbstatistics

    7 жыл бұрын

    Thanks! You never know what the future might bring :)

  • @hibashahid948
    @hibashahid9483 жыл бұрын

    THANKK YOUU ♥️

  • @fahada1921
    @fahada19217 жыл бұрын

    i cant thank you enough.

  • @abromchris7670
    @abromchris76705 жыл бұрын

    As I opened my Chinese Version book of probability in Gausion's distribution chapter. I thought...w*f but after your explaination... Thx

  • @prakashlamichhane5802
    @prakashlamichhane58027 жыл бұрын

    how could we know that 0. 1 lies on left but not on the right part please explain i couldn't understand

  • @huntersikari
    @huntersikari8 жыл бұрын

    Hello Thank you for the videos Can anyone please tell How we can calculate this expression " P(-1.72

  • @huntersikari

    @huntersikari

    8 жыл бұрын

    Got it ,,we have some table with values!

  • @pikapikacheww_

    @pikapikacheww_

    4 жыл бұрын

    @@huntersikari care to explain how to get area for -1.72 ?

  • @matt5931

    @matt5931

    Жыл бұрын

    @@pikapikacheww_ If using R you could write: pnorm(1.22) - pnorm(-1.72) to get the %. -1.72 and 1.22 are Z scores (x-mean/sd) for each side. I am terrible at explaining and 2 years late but I hope this helps someone.

  • @nped5054
    @nped50543 жыл бұрын

    How would you calculate the probability of the exercise with the adult American female and her height if the equation said P(150.5 < X -10 < 170.5)?

  • @jbstatistics

    @jbstatistics

    3 жыл бұрын

    Isolate X by adding 10 everywhere, then apply the same techniques from this video.

  • @wannorshaz
    @wannorshaz3 жыл бұрын

    Can I ask what if the question is "Ten texpayers are selected at random. What is the probability that 3 of the taxpayers will get their refunds at least 16 weeks?" but before this question it alreasy state that the average is 12 and stdev 3..the variable is the amount of time.. Can I know how to calculate it.. Thank you

  • @cristopherdjonovic7230
    @cristopherdjonovic72308 жыл бұрын

    How did you get get .846?

  • @InstansVisio

    @InstansVisio

    8 жыл бұрын

    +MadMax and how do u get 0.111 ?

  • @jbstatistics

    @jbstatistics

    8 жыл бұрын

    +Killan TRAPSA I have videos outlining how to find areas under the standard normal curve. You can use software or a standard normal table to find that area.

  • @mobilbear

    @mobilbear

    7 жыл бұрын

    see how it is calculated: See, P(Z1-1.72)=0.9573, what you actually want is the Z1 and Z2. Because the left side of Z2 = 1-Z2 = 0.0427, and we would know that the "AND" part will be Z1 - (1-Z2) = 0.8888-0.0427=0.8461

  • @mobilbear

    @mobilbear

    7 жыл бұрын

    +Killan TRAPSA1, because in the previous example, it is to ask P(Z>1.22), while, actually from the Normal Distribution value table, you can get 1.22 as 0.8888, which means value smaller than 1.22, as you already knew that the total shadowing is 1, then the P(Z>1.22)= 1-0.8888=0.1112, hope this helps

  • @wiiliskaako5875

    @wiiliskaako5875

    6 жыл бұрын

    you subtract 0.047 from 0.8888 and if u r asking how i got this numbers its the area of -1.72 and 1.22

  • @lindaren9467
    @lindaren94673 жыл бұрын

    Going through almost all your videos, haha.

  • @jenniepher87
    @jenniepher875 жыл бұрын

    thank you !!

  • @jbstatistics

    @jbstatistics

    5 жыл бұрын

    You are very welcome!

  • @marislox1844
    @marislox18444 ай бұрын

    where on earth did you get the -1.28? I cannot find any table that says this. Please, anyone?

  • @jbstatistics

    @jbstatistics

    4 ай бұрын

    It's the 10th percentile of the standard normal distribution, found with software or a standard normal table.

  • @simonpaisley101
    @simonpaisley1015 жыл бұрын

    How do you find the -1.28 using software though? (ie. using R). I understand how to get the value from the standard normal table but I don't know the formula in R. Do you know the formula?

  • @jbstatistics

    @jbstatistics

    5 жыл бұрын

    The R command qnorm(.1) returns -1.281552 (the 0.1th quantile of the standard normal distribution). qnorm(.1,0,1) would also work (returning the 0.1th quantile of a normal distribution with mean = 0 and SD = 1, which is of course the SND).

  • @simonpaisley101

    @simonpaisley101

    5 жыл бұрын

    @@jbstatistics Thank you so much! That helps a lot!

  • @ellybellyshin
    @ellybellyshin8 ай бұрын

    I dont get where did you get 0.846 in q2, I know its from the table but where.. and how..

  • @wiloabdi6516
    @wiloabdi65165 жыл бұрын

    Good presentation

  • @jbstatistics

    @jbstatistics

    5 жыл бұрын

    Thanks!

  • @fikrisaoudi7542
    @fikrisaoudi75428 жыл бұрын

    ur simply awsome thnx

  • @jbstatistics

    @jbstatistics

    8 жыл бұрын

    +Fikri Saoudi You are very welcome!

  • @twessyrasmijn420
    @twessyrasmijn4202 жыл бұрын

    I still did not get how you ended up with the 0.11 probability. can you please explain how can I calculate the probability of 0.11

  • @mherignatosyan2053
    @mherignatosyan20534 жыл бұрын

    What software can I use

  • @537yaya
    @537yaya9 жыл бұрын

    Hi can you elaborate more on how you found the area for the second example (around 7:42) with the P(-1.72

  • @jbstatistics

    @jbstatistics

    9 жыл бұрын

    P(-1.72

  • @jordanpeterson2800

    @jordanpeterson2800

    9 жыл бұрын

    jbstatistics Don't quite understand how you came up with 0.846 out of -1.72 and 1.22 at the 8:00 mark. Could you elaborate?

  • @alix14359

    @alix14359

    8 жыл бұрын

    +jbstatistics please would you be able to explain this

  • @mobilbear

    @mobilbear

    7 жыл бұрын

    +1, i don't understand either, please help to answer, thanks

  • @mobilbear

    @mobilbear

    7 жыл бұрын

    ah! i got it. +537yaya, +Jordan, +Alix, See, P(Z1-1.72)=0.9573, what you actually want is the Z1 and Z2. Because the left side of Z2 = 1-Z2 = 0.0427, and we would know that the "AND" part will be Z1 - (1-Z2) = 0.8888-0.0427=0.8461

  • @mehrbanoo5202
    @mehrbanoo5202 Жыл бұрын

    thanks

  • @Moviper43
    @Moviper4310 жыл бұрын

    Hi can you help he solve this question. ..if a mean is 280 and sd is 12..in a normal distributed random variable. .what's the probability between 275 than 290

  • @jbstatistics

    @jbstatistics

    10 жыл бұрын

    I suggest you watch the example in this video that starts at 5:50. Cheers.

  • @ShirinTejani
    @ShirinTejani8 жыл бұрын

    Hi, just wanted to confirm, the std. deviation if 6.8 is a value given in the question on 10th percentile calculation. Or is it something that is calculated from somewhere?

  • @jbstatistics

    @jbstatistics

    8 жыл бұрын

    +Shirin Tejani That was a given -- it represents the true standard deviation of heights of adult American women. (In reality, the true standard deviation is unknown. The value given here is based on sample data, but is likely very close to the true value. In this question we are pretending that the true standard deviation is a known quantity.)

  • @ShirinTejani

    @ShirinTejani

    8 жыл бұрын

    +jbstatistics Thanks! (PS - the videos are really great!)

  • @jbstatistics

    @jbstatistics

    8 жыл бұрын

    +Shirin Tejani Thanks! I'm glad you find them helpful!

  • @sdvlog6335
    @sdvlog63354 жыл бұрын

    I do not know how did you get the 0.111

  • @caominh2874
    @caominh28742 жыл бұрын

    How did you get 0.111?

  • @Ahmad-zq8ve
    @Ahmad-zq8ve4 жыл бұрын

    what did you do to find 0.846 ???

  • @minjeonkim9655

    @minjeonkim9655

    3 жыл бұрын

    ye im also wondering

  • @nostro1940

    @nostro1940

    2 жыл бұрын

    Think about it, the whole area to the left of 1,22 is 76% You need to subtract the area to the left of -1,72 (which is 4,2%) to get the total area of 72,15% He is wrong

  • @agarciasanz
    @agarciasanz10 жыл бұрын

    Sorry, why do you say that by subtracting the mean from X you necessarily get a new mean of 0? I lost you in that reasoning. Thanks! (Very helpful videos)

  • @jbstatistics
    @jbstatistics11 жыл бұрын

    We can find the appropriate areas using software or a standard normal table. I have a playlist "Using a Standard Normal Table" which contains videos for the two main table types. Cheers.

  • @nelsonsinglhs
    @nelsonsinglhs7 жыл бұрын

    Your videos have been fucking helpful for my short summer class. THANK YOU!

  • @jbstatistics

    @jbstatistics

    7 жыл бұрын

    You are very welcome!