Total Volume of rainfall for that storm event
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.
To calculate the area under a hydrograph curve, you can use numerical integration techniques, such as the trapezoidal rule. First, divide the hydrograph into segments, typically between time intervals where flow rates are measured. Then, for each segment, calculate the area as the average of the flow rates at the two endpoints multiplied by the time interval. Finally, sum the areas of all segments to obtain the total area under the curve, which represents the total volume of water passing a point over the specified time period.
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.
100%
The area under the standard normal curve is 1.
Please see the link under "legitimate probability density function".
The total area under the density curve for a continuous random variable must equal 1. Given that the area from 0 to 5 is 0.00625, the area from 5 to 800 can be calculated by subtracting this value from 1. Therefore, the area under the density curve from 5 to 800 is (1 - 0.00625 = 0.99375).
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.