What is the standard error of the mean in analytical chemistry?

[Sir]

in my analytical chemistry review, this question cropped up. the first part was simple, but the second part has me confused to no end. I've tried playing around with the math as well as scouring my textbook for answers. help!

what is the probability that a single determination of a value is further below the mean than 2 standard deviations?

this part is the simpler part, given the table at the bottom of http://64.233.167.104/custom?q=cache:bdW_K0aRhzEJ:www.palgrave.com/business/taylor/taylor1/lecturers/lectures/handouts/hChap5.doc+chart+area+beneath+normal+curve+standard+deviations&hl=en&ct=clnk&cd=7&client=pub-8993703457585266" page.
the answer turns out to be 2.28%

the second part of the problem is: what is the probability that the average of 4 determinations is further below the mean than 2 standard deviations?

the answer was given to be 0.0032% but i cannot figure out where this value comes from.



ps. my apologies for not reading the sticky, I'll post this in the proper forums now.

 

[EnumaElish]

See http://en.wikipedia.org/wiki/Standard_error_(statistics) (look under "standard error of the mean").

 

[tacman]

The standard error of the mean in analytical chemistry is a measure of the variability of the sample means from the true population mean. It is calculated by dividing the standard deviation of the sample by the square root of the number of samples. It is used to estimate the range within which the true population mean is likely to fall.

As for the second part of the question, the probability that a single determination is further below the mean than 2 standard deviations is 2.28%. This means that if you were to take a random sample and make a single determination, there is a 2.28% chance that the value you get will be further below the mean than 2 standard deviations.

Now, for the average of 4 determinations, the probability is much lower because you are taking the average of multiple values. This means that the variability is reduced and the probability of getting a value further below the mean than 2 standard deviations is also reduced. The value of 0.0032% comes from the calculations for the standard error of the mean, which takes into account the reduced variability due to the multiple determinations. This probability is much lower because it is less likely to get a value further below the mean when taking the average of 4 determinations compared to just one determination.

I would recommend reviewing the calculations for the standard error of the mean and the concept of variability in multiple determinations to better understand where the value of 0.0032% comes from. Additionally, consulting with your professor or a tutor may also help clarify any confusion you have.