Uploaded November 2012 | Updated September 2026, 2 hours ago
I show how to find percentiles and areas for the F distribution using the F table. In the first part of the video I work through examples finding areas and percentiles in the right tail of the distribution. (These are often of more importance to us than the left tail values.) In the second part of the video I show the mathematical "trick" that allows us to find left tail values from a table that gives only right tail values, and work through examples.
I show how to find percentiles and areas for the F distribution using the F table. In the first part of the video I work through examples finding areas and percentiles in the right tail of the distribution. (These are often of more importance to us than the left tail values.) In the second part of the video I show the mathematical "trick" that allows us to find left tail values from a table that gives only right tail values, and work through examples.








![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:
http://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 The Sampling Distribution of the Sample Mean](https://i.ytimg.com/vi/q50GpTdFYyI/mqdefault.jpg)

![An Introduction to the Binomial Distribution
An introduction to the binomial distribution. I discuss the conditions required for a random variable to have a binomial distribution, discuss the binomial probability mass function and the mean and variance, and look at two examples involving probability calculations.
The estimated probability of a 90 year old Canadian male surviving for one year was taken from Statistics Canada life tables, which can be found at http://www.statcan.gc.ca/pub/84-537-x/4064441-eng.htm. The probability given in the table is the estimated probability that a randomly selected Canadian male, given survival to his 90th birthday, survives until his 91st. I simplified this explanation a little in the example in the video.
For those using R, here is the R code to find the probabilities for the examples in this video:
Die roll example.
Finding the probability of getting exactly two fives in three rolls:
dbinom(2,3,1/6)
[1] 0.06944444
Twenty randomly sampled 90-year old Canadian males example.
Finding the probability that exactly 18 survive for at least a year:
dbinom(18,20,.82)
[1] 0.1729609
Finding the probability that at least 18 survive for at least a year:
dbinom(18,20,.82)+dbinom(19,20,.82)+dbinom(20,20,.82)
[1] 0.2747932
or
1-pbinom(17,20,.82)
[1] 0.2747932 An Introduction to the Binomial Distribution](https://i.ytimg.com/vi/qIzC1-9PwQo/mqdefault.jpg)