Who invented normal distribution curve

Then as the frequencies approach zero, slope of the histogram also approaches zero, and the curve levels off as we get into the tail end of the curve. This gives us the following. Definition : Data are said to be normally distributed if the rate at which the frequencies fall off is proportional to the distance of the score from the mean, and to the frequencies themselves.

In practice, the value of the bell shaped curve is that we can find the proportion of the scores which lie over a certain interval. In a probability distribution, this is the area under the curve over the interval: a typical calculus problem. However, in order to use calculus to find these areas, we need a formula for the curve.

We can find such a formula because our definition gives us the following differential equation. Where k is a positive constant. Note that to the right of the mean, the curve will be decreasing and to the left, it will be increaing. We can separate the varaibles. The question now becomes, what is C , not to mention, what is k? We can use the fact that the normal distribution is a probability distribution, and the total area under the curve is 1.

If f x is a probability measure, then. This is actually somewhat humorous. It is a function which does not have an elementary function for its integral. Howe ever, there is a trick for getting the total area under the curve. First, let. Square the integral. Therefore, to solve this problem, you compute the probability of 60 heads, then the probability of 61 heads, 62 heads, etc. Imagine how long it must have taken to compute binomial probabilities before the advent of calculators and computers.

Abraham de Moivre, an 18th century statistician and consultant to gamblers, was often called upon to make these lengthy computations.

Binomial distributions for 2, 4, and 12 flips are shown in Figure 1. This is exactly what he did, and the curve he discovered is now called the "normal curve. Figure 2. The Varieties of Normal Distribution Demo allows you to enter values for the mean and standard deviation of a normal distribution and see a graph of the resulting distribution.

A frequently used normal distribution is called the Standard Normal distribution and is described in the section with that name. The binomial distribution can be approximated by a normal distribution. The section Normal Approximation to the Binomial shows this approximation. The Normal Approximation Demo allows you to explore the accuracy of this approximation. Belmont, CA: Duxbury. Google Scholar. Mitrushina, M. Handbook of normative data for neuropsychological assessment 2nd ed. New York: Oxford University Press.

Slick, D.