Normal Distribution, Z Scores, and Normal Probabilities in R | R Tutorial 3.3| MarinStatslectures

Normal Distribution, Z Scores, and Normal Probabilities in R: How to calculate probabilities, quantiles, percentiles and taking random samples for Normal Random Variables in R with examples. 👉🏼Normal Distribution concept in statistics: goo.gl/g9A1i5 👍🏼Best Statistics & R Programming Language Tutorials: ( goo.gl/4vDQzT )
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In this R video tutorial, we will learn to calculate probabilities for Z scores. we will also learn to calculate probabilities for a normal distribution using pnorm, dnorm, rnorm, and qnorm functions in R Software. This R tutorial will also show you how to draw the probability density curve for a normal variable.
This video is a tutorial for programming in R Statistical Software for beginners using RStudio.
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[@marinstatlectures]

In this R video tutorial, we learn to calculate probabilities for Z scores and draw the probability density curve for a normal variable. we will learn to use pnorm, dnorm, rnorm, and qnorm functions in R Software. Watch our tutorial on the concept of Normal Distribution, Z-Scores & Empirical Rule in Statistics: goo.gl/g9A1i5 ✍🏼If Like to support us you can Donate (bit.ly/2CWxnP2), Share our Videos, Leave us a Comment, Give us a Like 👍🏼 or write us a review! Either way We Thank You!

[@marcelovhm1]

Great stuff, great stuff. In the end I felt like the universe just opened up to me, haha!

[@Cherriheart]

I'm completely new to R and these videos have been so incredibly helpful for my stats course. Thank you!

[@marinstatlectures]

good to hear +BlueBird

[@greta1114]

So helpful! Thank you so much!

[@kexinma6610]

Hi Marin, NICE video and I am learning R by myself and now cant stop learning with your viedos. One of the suggestion for that is to add some background knowledge about stat so that will help us better understanding the consept of the graphs. Thanks!

[@kachan1457]

I really wanna thank you for this video, i've been stuck on something for hours and you explained it so clearly, sincerely thank you!

[@marinstatlectures]

great to hear, you're welcome!

[@javi19841000]

Great videos, really love them ... Excellente work... I am falling in love with RStudio even more!!!!! Thank you very much

[@ThijsGieb]

Thank you so much for this simple and clear tutorial!

[@marinstatlectures]

you're welcome Thijs Gieben

[@Jack-mv8iq]

Thanks, you saved my life, Sir... I was struggling with probability in R for my exam, which is tomorrow. And this video helped me a lot...🙏🙏🙏

[@carlosalfonso5829]

Your videos are the best, R its quite powerful

[@dawood_analytics]

finally, I found my teacher. you r great sir

[@marcoventura9451]

Very interesting as usual. We can add che Cumulative Probability plot of the CDF: cuml=pnorm(x, mean=75, sd=5) plot(x, cuml, type="l")

[@justaguy168]

This was a great video! Concise and powerful, just like R itself. What is confusing is that the p functions like pnorm and ppois compute cumulative probabilities given a quantile. The q functions like qnorm and qpois compute quantiles given a probability. You use the word percentile and probability interchangeably. Perhaps some clarification of terms is in order here.

[@samiradilrubaali5917]

how will i get the P(3

[@alpstinger5083]

thanks a lot for this video. I just had one doubt - what does the y axis in the probability density curve tell?

[@vladimirrosillo]

Thanks, very useful video!

[@benxu8112]

Thank you for sharing.

[@yanishappadoo9067]

How to perform a binomial/normal/poisson distribution on the dataset?

[@iVNa09]

Thank you!

[@kimicheng5611]

OMG this video is so helpfulllllllllllllllll!!!!

[@nz3018]

Hello Marin,Your tutorial are very easy to follow. Can you please make one on Propensity score matching. I ma struggling with this model.Thanks,Regards

[@myfirstarticle5120]

great video, thanks!

[@BazzTriton]

Muito bom. Obrigado

[@alebasicunha]

This was very helpful, thanks!

[@marinstatlectures]

Bela Cunha you're welcome, glad you found it helpful!

[@dianacarolinasuarez1548]

excellent video, very well explained!

[@marinstatlectures]

thanks +Diana Carolina Suarez !

[@eceserin]

I wish you were my stat lecture, I cannot believe youtube is better than a uni in US.

[@marinstatlectures]

These videos support a course I teach at The University of British Columbia in Canada, so you can transfer here :)

[@eceserin]

​@@marinstatlectures if I get an A+, its a deal :)

[@thatocyberspace]

I am so disappointed my favorite outro is not included in this video. The outro keeps me going all the time and that is why I love it.

[@marinstatlectures]

These earlier videos were before our son could talk. He started adding to our videos after a few years. He will be happy to hear you like his outros :)

[@SampurnR]

Thanks for the refreshingly clear video tutorial.. One thing, though.. The command: pnorm(x = 85, mean = 75, sd = 5, lower.tail = F) will calculate the P(X > 85) and not P(X >= 85)

[@marinstatlectures]

Thanks for your comment +SampurnR . For a continuous numeric variable (like the normal distribution), P(X=85)=0 , and so P(X>85) = P(X>=85)

[@mgultas]

R's output for P(X = 85) in a distribution with a mean of 75 and sd of 5. So how come P(X > 85) == P(X >= 85)? > dnorm(85, mean = 70, sd = 5) [1] 0.0008863697

[@marinstatlectures]

Hi +Mehmet Gültaş , what R is returning there is the height of the density/probability curve...the probability is the area under the curve. (e.g.) the probability P(84.5

[@mago2007]

Great channel! It´s super clear and very wel explained! Thank you! I have some doubts about this video. Searching the z score table the value 0.158 is assigned to z = -1.00, so I think you have calculated the value of the lower tail to -1. Am I right?

[@marinstatlectures]

Hi, for a Z table (giving values below -Z) you can find that P(Z < -1) = 0.158 (or the area below Z=-1 is 0.158), and also P(Z>1) = 0.158 (or the area above Z=1 is 0.158). since the standard normal (Z) is symmetric about 0, the area below -z is the same as the area above +z. i hope that clears it up...

[@raguspag55]

How do you correlate zscores to sigma ? In other words , how do you know that the probability is random or not chance occurance?

[@mallikarjunreddy-arjun4678]

I have dataset in that lcl and ucl observed values are there,soi need pass qic package to plot a graph how?

[@malmulkalil4546]

good vid

[@kennethgituro7578]

awesome job i have learnt alot. i didnt know are until i watched your video. so what is the formula of determining the probability of a football match?

[@marinstatlectures]

lol, it's more complicated that that :) but a good starting point is learning either about regression models (logistic), or different classification models (such as decision trees, and other sorts of machine learning type algorithms).

[@SNPolka56]

Great Lectures.

[@marinstatlectures]

thanks +Unver Hosayn !

[@zakariahaddouche2922]

hey there, this is so awesome. i wonder how can i calculate a probability of a number being between tow limits (upper and lower), and not just lower tail and upper tail?

[@marinstatlectures]

Hi +Zakaria haddouche , as an example, suppose that you want to calculate the probability that X is between 70 and 80, for a normal with mean=75, SD=5, you can just calculate the probability that X is less than 80, and then subtract/remove the probability that X is less than 70 from that, (e.g.) *pnorm(80, mean=75, sd=5, lower.tail=T) - pnorm(70, mean=75, sd=5, lower.tail=T)*

[@zakariahaddouche2922]

ya that's what i did but i was wondering if there is an other direct method. thank you so much. otherwise, i sent you an e-mail i hope you've seen it.

[@sasikanthpenumadula8829]

Lets say a coin is tossed 500 times and i want to know what is the probability of heads between 250 and 260. On the paper I can calculate mean and standard deviation and use it like you mentioned in the above comment. However is there a formula in R to calculate mean and SD and also get the actual probability for my question? Thanks

[@poojarathod3652]

How to find percentage of area under curve before or after that vertical line? At 5:33

[@raahinakhetani7498]

How do we fit a normal distribution to a numerical attribute?

[@bhara033]

Hi, Marin! The sequence generated to apply dnorm to does not have a sd=5. Can you please explain? Thanks!

[@marinstatlectures]

those are the x-values only. the dnorm command is then used to find the y-values for a normal distribution with mean 75, sd=5, that correspond to those x-values

[@kalyanaravalli]

Hey Marin, nice video. How to divide all the column values in a csv file with a particular value

[@marinstatlectures]

Thanks +Kalyan Ramanuja. If you want to divide the entire matrix by some constant, c, then you just enter *data/c*, and this will divide everything by "c". if you wanted to divide only the 3rd column of the data by the constant c, you can enter *data[,3]/c*

[@kalyanaravalli]

Hey Martin, Thanks for the help. When I do data/c, this is the error : non-numeric argument to binary operator I got.

[@marinstatlectures]

Hi Kalyan Ramanuja , you should enter a number for "c", not "c" itself. (eg) to divide everything by 2, enter *data/2*. the "c" was meant to be generic, where you enter the value of c that you want.

[@kalyanaravalli]

Hi +MarinStatsLectures, I know that I am trying to divide a dataset with a vector that consists of two values(56, 89).

[@aadityanr8556]

@@kalyanaravalli How does the math work there?

[@horiapopa6341]

Hi Mike, I have a question. How is "rand" normally distributed? It is a set of numbers, with a min of 55, max of 95 and a mean of 75. All the numbers are evenly distributed, there is the same interval between all of them, .25. What is the meaning of "probability density" in this case? Why is the probability density of 60 smaller than that of 70? Thanks, Horia

[@marinstatlectures]

Hi Horia, you've mixed two things together there. first, i created an object "x" that was a sequence from 55-95, with a spacing of 0.25 between them,..these are uniformly distributed. i then used the "dnorm" command to find the height of the density curve for the normal, for these values of "x". the probability density, is the "f(x)" ( as opposed to the cumulative distribution function, F(x) = P(X

[@horiapopa6341]

Thanks for the reply. I was under the impression that in analyzing data one has to check first if there is a normal distribution in the variable, in order to use the right process. Here it seemed counterintuitive, to me, that you created that set (x) and then found the height of the density curve. My thinking is that if this were a normal distribution, 68% of the numbers would fall between 70 and 80 but that is just not the case. Anyway, I don't want to take your time. Thank you for your videos and I have to say that your icon picture is absolutely amazing!

[@randomfandom33]

There's a mistake here. For P(x>=85), you must write pnorm(x=84, mean=75, sd=5, lower.tail=F). This is because when the lower.tail argument is set to FALSE, you get the probability of x > k (where k is the number you want), not x >= k. So setting x = 84 will give us the probability of 85 and above.

[@rishikesh330]

Was there any specific reason why you chose sd=5 at 4:35?

[@marinstatlectures]

Hi +rishikesh pandey , no particular reason, in the video ive used an example of a normal distribution with a mean of 75 and a SD of 5. this was an arbitrary choice of values that ive used throughout the video.

[@Kaysar777]

So this is what is used for Value at Risk.

[@anshulsharma343]

just wanted to confirm whether lower.tail=T is for only less than (=. > ppois(q=9,lambda=7,lower.tail=T) [1] 0.8304959 > 1-ppois(q=9,lambda=7,lower.tail=F) [1] 0.8304959 I tried this and if both T and f includes the value 9, then the answer would not have been same

[@xuejieyu]

So why the histogram in the end doesn’t look normal? Not enough sample size?

[@marinstatlectures]

that's correct...when the sample size is small, the histogram will not look exactly like the true shape of the population. you can imagine, if you take only n=2 observations from a normal population, the histogram of those 2 observations can not look normal....if you took n=10, it will look a "bot more normal", but still n is too small for it to look 'perfectly normal'. as n gets larger, the histogram of those n observations should look more and more like the shape of the distribution for the population.