The Sampling Distribution of the Sample Mean

I discuss the sampling distribution of the sample mean, and work through an example of a probability calculation. (I only briefly mention the central limit theorem here, but discuss it in more detail in another video).

The mean and standard deviation of the amount of protein in a quarter pound patty of lean beef was found in the USDA nutrient database at:

For those using R, here is the R code to find the values in the examples:

The probability a randomly selected patty has at least 23.0 grams of protein (mu = 21.4, sigma = 1.9):
1-pnorm(23.0,21.4,1.9)
[1] 0.1998645
or, if we standardize:
1-pnorm((23.0-21.4)/1.9)
[1] 0.1998645

The probability that the mean of 4 randomly selected patties is at least 23.0 grams of protein (sampling from a normal distribution with mu = 21.4, sigma = 1.9):
1-pnorm(23.0,21.4,1.9/sqrt(4))
[1] 0.04607049
or, if we standardize:
1-pnorm((23.0-21.4)/(1.9/sqrt(4)))
[1] 0.04607049

[emem]

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[Explorer]

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[jbstatistics]

Thanks, I'm glad you like my videos.

Thanks for the suggestions. Gamma, Weibull, and lognormal are definitely somewhere on the horizon, but it will be a little while before I can get to them. (I've got a number of other videos lined up right now.) Cheers.

[dasgomezkanal]

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Anyway, I really just wanted to thank you a lot for your help. This is my last semester as an undergrad and without these videos I don't think I could pass this subject and graduate.
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[rien]

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[hugocpl]

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[os]

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[radhikamamidi]

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[WRONGTURN]

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[hessaa]

I really like your way in explaining its very simple and understandable.

I hope that you create a video tutorial for Gamma, Weibull and Lognormal distributions because I didn't find any good video tutorials for these concepts.

Thanks in advance =)

[physiciansmind]

Awesome video. This provided great help for my upcoming stats exam!

[chumpapii]

Hey man what if thre are 2 given sample mean like between 445 and 485?

[leahhall]

this is the video that made everything make sense in my head

[superkamiguru]

My teacher never teaches in class so i'm forced to scour the internet and search for problems similar to the work he gives out to help me understand it better. After watching this video, I still am at a lost for what to do

[ItsASoccerTing]

how did he get from 0.8 to 0.2 in the first example

[jeeruajay]

I have one doubt, x' mean is equal to population mean when we take mean of the sampling means otherwise not ? but your told that only one sample mean is equal to the population mean how tell me ?

[katieandrews]

Thanks for the videos! Like another commenter, I can't seem to figure out how you got 0.200 at the time mark of 7:20 in your video.

[letseconomics]

@8:39 why do we choose the middle data? We have to draw a sample of size 4 so we can take four values from the left or right as well? And will the mean will be the same as 21.4 for all samples we draw from this distribution?