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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.
What else can I help you with?
The total area under a normal distribution is infinite?
The total area under a normal distribution is not infinite. The total area under a normal distribution is a continuous value between any 2 given values. The function of a normal distribution is actually defined such that it must have a fixed value. For the "standard normal distribution" where μ=0 and σ=1, the area under the curve is equal to 1.
Is The total area under the curve of any normal distribution is 1.0?
yes because 1 = 100% so the entire area under the curve is 100%
Is in the normal distribution the total area beneath the curve represent the probability for all possible outcomes for a given event?
Yes. The total area under any probability distribution curve is always the probability of all possible outcomes - which is 1.
What is the area under normal distribution curve between z1.50 and z2.50?
Approx 0.0606
What is the area under the standard normal distribution curve between z1.50 and z2.50?
~0.0606
The total area under a normal distribution is infinite?
The total area under a normal distribution is not infinite. The total area under a normal distribution is a continuous value between any 2 given values. The function of a normal distribution is actually defined such that it must have a fixed value. For the "standard normal distribution" where μ=0 and σ=1, the area under the curve is equal to 1.
Is The total area under the curve of any normal distribution is 1.0?
yes because 1 = 100% so the entire area under the curve is 100%
Is the total area under a normal distribution curve to the right of the mean is always equal to 0?
100%
If the tails of the normal distribution curve are infinitely long. Is it True or False that the total area under the curve is also infinite?
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.
Is in the normal distribution the total area beneath the curve represent the probability for all possible outcomes for a given event?
Yes. The total area under any probability distribution curve is always the probability of all possible outcomes - which is 1.
What is The area under the normal curve to the right of mu and mu equals?
In a standard normal distribution, the area under the curve to the right of the mean (mu) is 0.5. This is because the normal distribution is symmetric around the mean, and half of the total area (which equals 1) lies to the right of the mean and half to the left. Therefore, for any normal distribution where mu is the mean, the area to the right of mu is always 0.5.
What is the area under normal distribution curve between z1.50 and z2.50?
Approx 0.0606
What is the area under the standard normal distribution curve between z1.50 and z2.50?
~0.0606
What is the area under the standard normal distribution curve between z0.75 and z1.89?
0.1972
Give three properties of a normal distribution function?
1.it is bell shaped.2.m.d=0.7979 of s.d 3.total area under the normal curve is equal to 1.
What is the area under the normal distribution curve to the right of z that equals 3.24?
0.0006 (approx).
What is the significance of the constant 1/sqrt(2pi) in the formula for the standard normal distribution?
The constant 1/sqrt(2pi) in the formula for the standard normal distribution is significant because it normalizes the distribution so that the total area under the curve equals 1. This ensures that the probabilities calculated from the distribution are accurate and meaningful.
