Sampling distribution example problem | Probability and Statistics | Khan Academy
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- Опубликовано: 8 фев 2025
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Figuring out the probability of running out of water on a camping trip
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Probability and statistics on Khan Academy: We dare you to go through a day in which you never consider or use probability. Did you check the weather forecast? Busted! Did you decide to go through the drive through lane vs walk in? Busted again! We are constantly creating hypotheses, making predictions, testing, and analyzing. Our lives are full of probabilities! Statistics is related to probability because much of the data we use when determining probable outcomes comes from our understanding of statistics. In these tutorials, we will cover a range of topics, some which include: independent events, dependent probability, combinatorics, hypothesis testing, descriptive statistics, random variables, probability distributions, regression, and inferential statistics. So buckle up and hop on for a wild ride. We bet you're going to be challenged AND love it!
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My Stats lecturer always got me bored and couldn't understand a thing, I skipped 9 statistics lectures this semester, now that I'm looking at vids from khan academy, stats is pretty fun... its just the matter of teachers we get
i skipped almost the whole semester but yeah he is interesting
lmao literally same comment did you go to Bama?
Always easy to make others responsible
@@SealSuperior no, most collage teachers suck
Also depends on whether or not you have any math ability. Sounds like you don't.
This is so good....
I've probably learnt more statistics by watching these videos than I would have ever learnt by reading my textbook...
PS: for those who didn't get it, watch his previous videos
What do I type to find your relevant recommendation? What is significance of Ux=U=2L?
This is gold! I have learned statistics all semester without going to professors lessons or even done anything else than doing old exams and practice problems. I have an exam two days from now and this helps me a lot, just to get my head around the actual concepts! I even didn't care to understand it very much, just did the math and got the answers right for the most part. But it's SO satisfying to understand the fundamentals, thanks yo you, SUPER TEACHER :D Greetings from Norway.
which uni you were from?
i feel like he tried so hard to make it simple that it actually went complicated
Nah! it's just a matter of perspective. You should watch previous lectures where he laid the foundation.
You are a fantastic teacher sir. I've been learning about sampling distribution through an online certificate course, and while the instructor may go in depth with the formulas and theory, you have really made it click for me by showing HOW the sampling distribution can be APPLIED to making decisions. Thank you so so much!
THANK YOU SOSOSOSOSO MUCH!!!!!!!!!! You are amazing!!!!!!!!!!!! I signed in just to comment and like the video!
Now my course material makes sense! Thank you!
Done thanks
Takeaway: when taking a sample from a normal distribution, the normal distribution of the sample has same meaning but different standard deviation related to the original distribution, based on the sample size. You can then calculate probabilities based on the sample’s normal distribution.
Var(S)=Var(X)/n where var(s) is new variance of the samples you took and var(x) is the variance of the distribution you are sampling from
It really helps a lot these two graph helps me figure out the relationship between The population distribution and simple distributions!
In this entire unit this video was the one which helped me understand what is going on.
Brilliantly broken down explanation; you absolute god
I am in shock in awe due to the awesomeness of your teaching abilities.
As a sacrificial gesture, I offer you my ex girlrfiend.
Yes! I'm so excited to see a statistics video from you in my subscription box.. you have a way of explaining statistics like no other.
The picture of an extremely skinny 50 cent in the ad kind of freaked me out throughout the whole video. He's piercing my soul
My stats professor always speaks so fast and doesn't explain much, I don't understand a thing. Your videos are so helpful and you teach a million times better.
Excellent. - And now... the probability that the world is facing a currency fight between nations...and the probability for US to get out save from this fight.
I understood the problem completely thank you very muh.
As a side question: couldn't we solve the problem by just multiplying the mean and standard deviation by 50 so we would get a normal distribuiton of N(100,35) and calculate P(X>110) ?
Thanks! Great explanation.
I think this is a great video. At times slow on calculations..but that should be pardoned I guess :). The key is that "distribution of sample mean is always Gaussian" when the no of samples is 'good enough'. Here is a trick question I thought of: How does the probability get affected if reduce the number of men to 25 instead of 50 and reduce the water to 55 L from 110 ? :)
The graphs he draws always mesmerize me.
this seems very countertuitive to what I thought.
My estimation were - since the mean consumtption for the popultaion was 2 with standard deviaiton of 0.7.
Without doing inferential statisitics - A size of 50 men would have mean comsumption of 100L with standard deviaiton of 35. That would mean a 110 L with have sort z score of +(110 - 100)/ 35 = +0.28 and on the z score table its about 0.6103. So chances of running out was 0.39 approx.
With inferentail statistics I though the probability of running out would rather increase for smaller size ?
Not talking mathmatical or analysis
if we would bring bring 5 liters of water for a group of 2 people on a trip(sort of like 2.5 per each) , for a gorup of 10 we would rather bring about 15 liters but inferentail stats would require to bring about 30 liters (thats 3lit per person) if we are to keep the same chance of running out. Wow doesnt that seem counterintuitive to what we normally do?
Exactly the mistake I did when I tried solving this one while pausing the video at the beginning. Maybe this is why we have a subject called statistics brother and yeah thinking again it seem pretty intuitive.
As we don’t know whether the distribution is normal or not, so z score tables doesn’t work here. The key is you can take any type of crazy distribution but the sample distribution of sample mean tends to approach normal distribution.
Probability of happening some event changes as we increase the observations or number of trials in any distrbution,,you can think of this in the same way since there are 50 men so chance any singleperson running out of water increases tbats why we have to consider greater quantity of water than our assumption...you cannot generallize probability whatsoever the situation is unless its specified
Ha haaa! I was struggling with this a few years ago. Now I rewatched the video and was able to do it by myself.
Thanks again Sal!! You are such a good teacher!
Thank you a 1000 times buddy
Very clear explanation. Thank you, very much.
When you want the sample variance, you use sigma^2/n and if you want the standard deviation, you take the sqrt of that, correct? If you're given sigma and n, can't you just use sigma and divide it by the sqrt of n to be the standard deviation when you use the formula?
I hope my question made sense.
Great, thank you
great explanation
you are a genius!
Fantastic explanation...as the rest of all videos. Maybe some structure is needed to get a base from that knowledge improvement can be progressive.
What if the original distribution itself is normally distributed. Say for example in this case if the original men and water problem itself is normally distributed. Then the P(run out) will be between 34-45%. However the final answer which is around 2.1% has so much error compared to 34-45%
definately a life saver
Thanks Sir
❤️❤️
Loved the explanation provided.....never felt stats could be this easy
Thank you Sir
Amazingly done... thanks alot I was having a trouble with that❤
God bless you Sal Khan!!, You are amazing
If y* is the average of the the sample you chose basically we search P(y*>2.2) ->
P{(y* - μ)/σ/sqrt(ν)>(2.2-2)/0.099}->
P(X=Z score>2.02)=1-P(X=Z score=
wish i had these statistics videos one year ago >.< ... ahh well these statistics videos are great and a great review :D thanks for uploading this
fighter jet!!!
also this was very helpful
Fun fact: the 1st standard deviation is the point of inflection on a bell curve (Sal's drawing is more just a hill)
hey you still have that cliff hanger on the currency series going, don't you forget to conclude that! We are waiting!!
bravo!!!
honestly, it's most easy to learn statics of class, I love it. Thank you!!!!
Nice explanations, but the pace can be a little bit faster.
No, it's just right.
Then, if you asume normality for each individual, you need to use a Sudent-t distribution instead of the Gaussian.
This problem can be done in a much simpler way though…
Uhhh how?
why aren’t videos in the playlist arranged properly ??
Is it a good habit to use normalcdf instead of looking up Z-scores?
Exactly I was so confused watching this because that's not how I was thought.
How does a distribution of values differ from a sampling distribution?
Sir please upload(if you have) a video on Generalized extreme value distribution. And if possible explain how to fit given data in it and how we can find all three parameter(scale,shape,location)
Thank you.
@Valem0r you wouldnt get a normal distribution if you multiplied by 50. you only get a normal distribution from the CLT.
So using the sample mean of the sample distribution is only necessary if you don't get a normal distribution?
Thijs Gieben Maybe it’s difficult to find a perfect normal distribution in the real world, numbers are irrelevant or other reasons, but using the sample mean can solve the problem, we don’t care whether it’s a normal distribution or not, as long as we choose samples and do a lot of trials, the sample means look like they follow the normal distribution. Does my explanation make sense?
Hmmm helpful :-)
this topic enforces how much i hate this subject, i literally cannot understand it
Why does the standard deviation of sample reduces with the increase in size of the sample while the sample mean has the same value as the population mean? I mean why is SDx = SD/sqrt(N) ?
good video but faster plz
Fast forward 1.5 times
why the sample variance is equal to population variance divided by n
Kindly watch the previous video(s), you'll get it :)
A little too scattered in the explanation for me. The volume is great, but honestly I hear him start a sentence and not finish it or explain the formula he's using to get these numbers. That would be helpful.
So even with the sample thats the probability for the main question on the amount of water until the 100 individuals run out?
Hi!. Thank you for the informative session. I have a question here. When you drew the probability distribution for all the men ( i.e. the first graph), the distribution being normal was uncertain. So we took the sample of sample size 50 and plotted the sampling distribution of the sample means. In this graph, the y axis shows the frequency of the sample means. Do we not have to have the probability function on the y axis to work out the further statistics like z score and all instead of the frequency? I am confused at this point. Basically how is the probability function P(x) different from frequency?
I thought he drew the probability distribution not the frequncy distribution
Good job, bro. I was once teaching this to my dumb ex wife (whose major was accountancy). And she didnt get a damn thing out of me. Maybe because I am engr :D
I'm confused--I thought the sigma was supposed to represent the population average and sigma_x-bar the standard deviation of sample means of size n taken from the total population. But then wouldn't that mean that n is not 50, because that would just be taking the whole population as our sample?
No the sample size is still 50. But since you commented this 7 yesrs ago I guess you've figured everything by now
love you
I could live my life without this nonsense subject.
jaimie deziel I'm taking it now. I've been up for about 24 hours with maybe 30min nap trying to complete homework. I'm so far behind because I'm so lost.
Stats is fun
😂😂😂
I already failed two times in a row😮
actually I wonder who would put dislike on such videos?
I'm going to get this question wrong for sure
some sort of fighter jet outside...lets just hope they dont come back..
LMFAOOO khan academy
Alright, but when do we use σ p-hat instead of σ x-bar?
p-hat is used to denote a sample proportion (which is the total # of things, like "how many 'yes' or 'no' responses are there")
x-bar is used to denote a sample mean (which is the mean of something , like "what is the mean annual salary for people over the age of 25 in Washington")
i want to know why no sound on this videos ?surely not all.
I am thirsty now.
"The average male" is a good way to start a statistics problem...
I had a doubt. How did we know that this was normally distributed?
Because a sample size of 50 from the population has a great chance of being normally distributed if it is been sampled several times
can we not use empirical rule here?
you could, but it would be an approximation rather than an exact estimation (which is just a better approximation though).
may anyone tell me where i can get a calculator software like that? i really need one
then your teacher is gonna tell you, '' sorry guys by error i forgot to write the value of the sigma , now you could just write it down... the value is...
is this Moivre's Theorem
Great explanation but very slow!
anyone know why the videos I watch on subscribed playlist doesn't show up in my watched history?
This is confusing. When are you taking the std dev value as it is, and when are you using the formula to calculate it! I mean the hypothesis test calculations (from previous lecture) are dfferent from these calculations.
I mean why when std dev of the population is already given as a value, 0.7L, did you calculate using the formula ??
Hi, muralidhar40. I'm almost certain he is calculating a separate standard deviation for the sampling distribution of the sample mean, also called the standard error of the mean.
The reason this is necessary is because the sampling distribution of the sample means is always going to have less variance than the original population distribution (the data won't be as spread out). Therefore, the standard error of the mean will always be a different value than the orginal population's standard deviation.
I'm probably not the best at explaining this, as I'm also currently studying, but I hope this can give some clarity!
I'm already thirsty at the 02.03 .... let me get some water
Why is it normal distribution?
Its part of the large sample theory I think
JUST TELL ME HOW TO ENTER THAT IN MY TI-84 PLUS.
Thumbs up if you could do 110/50 instantly 🤓🤓🤓
I drink four liters everyday . Basically one gallon of water 😂 I had no idea I was in the high percentile
(03:51) funny technical error .. if we are right on the money, we *will* run out of water. I think what you mean to say, it's *okay* because nobody that day wants to drink *more* than we have available / we have enough to satisfy everybody. [and besides it's a continuous random variable, so same probability either way, X > 2.2 or X- => 2.2]
I have a question, I fail to see how the answer you have given is related to the answer that was required.
You have calculated the probability of a Random Variable X, with a distribution that you have over there, takes the value greater than 2.02, not that the mean of it is greater than 2.02? Maybe it's just me but I fail to see how the mean of 50 [means of liters consumed by man] is defined by the distribution function you proposed?
By observation and intuition the mean of the sample size and the sampled mean are not far apart , if the sampling is done more times you might approach the exact mean of the sample size so it makes sense to assume The sampled mean to be sample size mean
Why do you divide 110 by 50? :)
110 liters of water, and there are 50 people. On avarage that makes 110/50=2..2 liters/man
🤔🤔🤔
all I need is to be active outdoors and I wont need more than two liters of water for the rest of my life :D
didnt understand the Z part
stats hells ye!
Why start mixing the names of things? Is it the standard deviation or variance? I hate math omg.
this guy is beating around the bush
Thumbs up if you're drinking water while watching this
Fighter jets hovering around your house.Haha.........
Nvm, I think I got it.
this dude eating up his own words, we need Indian math video
I'm sorry you could you repeat that statement? I didn't hear it the first 5 times you said it.
why is it sample? isnt it populatioN?
Because in statistics we rarely have the whole population. Here the 50 men is a sample of the whole population estimated at 7.4 billion. It is a lot easier to use a sample than a census.
such a smart but indecisive man lol
this video ( #29 ) is wrong. You cannot take ONE random sample size 50 of a population and expect it to have a lower standar deviationthan than the population. It is a misinterpretation of the central limit theorem which requires the the probability distribution of the means of N samples size n, not just one sample size n.