Uploaded September 2013 | Updated September 2026, 2 hours ago

---

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:

ndb.nal.usda.gov/ndb/foods/show/7413?fg=&man=&lfacet=&format=&count=&max=25&offset=&sort=&qlookup=beef+hamburger

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