The integral of the density with respect to the variable against which the density is plotted, between the values at the ends of the curve.
Since there is no information given as to what the density is plotted against, a more informative answer is impossible.
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 a symmetric function which is fully described by two parameters. It is called bell shape but I have never seen a bell whose rime is infinitely far away from its apex. The area under the curve is equal to 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.
It is any shape that you want, provided that the total area under the curve is 1.
False. A normalized distribution curve (do not confuse normalized with normal), by definition, has an area under the curve of exactly 1. That is because the probability of all possible events is also always exactly 1. The shape of the curve does not matter.
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).
yes
Total Volume of rainfall for that storm event
A density curve is a graphical representation of the distribution of a continuous random variable, illustrating how probabilities are distributed across different values. It shows the shape of the data and ensures that the total area under the curve equals one, reflecting the total probability. The area under the curve between two points indicates the probability of the variable falling within that range. Density curves can take various shapes, such as normal, uniform, or skewed, depending on the underlying data distribution.
100%
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
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 a symmetric function which is fully described by two parameters. It is called bell shape but I have never seen a bell whose rime is infinitely far away from its apex. The area under the curve is equal to 1.
There is no histogram below.However, the area under the curve for any histogram is the total frequency.
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%.
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.