: Bottle/can fillers don't always put the same amount of liquid in the container. Thus, the variability in the amount which we assume to be uniformly distributed. Pay attention to 0:34 and 0:43.
Bottle filler : Bottle/can fillers don't always put the same amount of liquid in the container. Thus, the variability in the amount which we assume to be uniformly distributed. Pay attention to 0:34 and 0:43.
Apple juice : Actual amounts of apple juice in a juice can that is supposed to have 1 litre of apple juice.
In the first class you wrote your heights (in meters) and handspans (in centimeters) on a sheet of paper. Here is what everyone wrote:
And here is how MegaStat analyzed these data (height and handspan data for all).
Exam marks : Normally distributed exam marks of a large class (475 students) from a few years ago. An easy method for checking normality is the normal curve plot: If it looks linear, then the data must be normal.
Binomial and normal : When n is large and p is around 0.5, binomial looks like normal. The next few links illustrate this.
Galton's Board: Here's what happens if you drop a large number of marbles in the board and p = 1/2. (Binomial turns into normal.) This link does it in real time.
Here is a Wikipedia article on the normal distribution.
IQ Scores (How X gets transformed to Z) : Transformation from X with mean μ = 100 and standard deviation σ = 15 to standardized Z with mean 0 and standard deviation 1.
Table of areas (under the standard normal curve from 0 to z) : This table (5.1 on page 156 and A.3 on page 651) can be used to calculate the normal probabilities from 0 to z.
Cumulative areas under the standard normal curve to z : This table (5.2 on pages 168-169 and A.4 on page 652) is slightly more convenient.
Standard & Poor's (S&P 500): There are 11 sectors totalling 500 companies.We look at one week returns (GICS Scorecard) and find this data set. (The weekly return information changes every week. The Excel file is from an earlier period.) The normal curve plot is almost linear, indicating normality. In fact, the histogram also looks like the normal distribution. Let's find the probability that you would lose money in one week if you invested in a randomly selected stock in the S&P 500 Index.
