Calculating probabilities in Normal distributionsIt may be interesting to familiarize ourselves with the probabilities correspondig to different intervals in normal distributions. Two points on the xaxis determine the extremes of the interval for which the probability is calculated (approximately) Different options A1, A2, ..., A6 correspond to different intervals that can be defined with those two points. Taken in pairs these are complementary in the sense that the sum of probabilities is 1. We can modify the parameters of the normal distribution and see how the probabilities vary. The gray dots control vertical and horizontal scales of the graphic. By pressing the right button and dragging we can move left and right. REFERENCES
George Marsaglia's article Evaluating the Normal Distribution.
LINKS
The Normal distribution was studied by Gauss. This is a continuous random variable (the variable can take any real value). The density function is shaped like a bell.
One important property of normal distributions is that if we consider intervals centered on the mean and a certain extent proportional to the standard deviation, the probability of these intervals is constant regardless of the mean and standard deviation of the normal distribution considered.
Student's tdistributions were studied by William Gosset(18761937) when working with small samples.
When modeling a situation where there are n independent trials with a constant probability p of success in each test we use a binomial distribution.
In some cases, a Binomial distribution can be approximated by a Normal distribution with the same mean and variance.
