Please see the link under "legitimate probability density function".
the standard normal curve 2
1 sigma does not represent 68.8 percent of anything.The area under the standard normal curve, between -0.5 and +0.5, that i, the central 1 sigma, is equal to 0.68269 or 68.3%.
What is the area under the normal curve between z=0.0 and z=1.79?
The area under the normal distribution curve represents the probability of an event occurring that is normally distributed. So, the area under the entire normal distribution curve must be 1 (equal to 100%). For example, if the mean (average) male height is 5'10" then there is a 50% chance that a randomly selected male will have a height that is below or exactly 5'10". This is because the area under the normal curve from the left hand side up to the mean consists of half of the entire area of the normal curve. This leads us to the definitions of z-scores and standard deviations to represent how far along the normal curve a particular value is. We can calculate the likelihood of the value by finding the area under the normal curve to that point, usually by using a z-score cdf (cumulative density function) utility of a calculator or statistics software.
The are under the curve on the domain (a,b) is equal to the integral of the function at b minus the integral of the function at a
Basically this isn't possible. Whenever you have an irregular curve, you need some kind of integration technique to get the area, or an estimate of the area. This can be quite simple, at least in principle: just approximate the area by narrow rectangles, calculate the area of each rectangle, and add everything up.
yes
Because the area under the curve is a probability and probabilities range from 0.00 to 1.00 or could also be written as 0% to 100%
It is not, if it is a graph of force against acceleration.
The area under the standard normal curve is 1.
100%
Please see the link under "legitimate probability density function".
If this is on mymaths.co.uk then the answer to this question is: Integration. That is how to find the area under the curve.
The area under the normal curve is ALWAYS 1.
Characteristics of a Normal Distribution1) Continuous Random Variable.2) Mound or Bell-shaped curve.3) The normal curve extends indefinitely in both directions, approaching, but never touching, the horizontal axis as it does so.4) Unimodal5) Mean = Median = Mode6) Symmetrical with respect to the meanThat is, 50% of the area (data) under the curve lies to the left ofthe mean and 50% of the area (data) under the curve liesto the right of the mean.7) (a) 68% of the area (data) under the curve is within onestandard deviation of the mean(b) 95% of the area (data) under the curve is within twostandard deviations of the mean(c) 99.7% of the area (data) under the curve is within threestandard deviations of the mean8) The total area under the normal curve is equal to 1.
If the values of the function are all positive, then the integral IS the area under the curve.