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The total area of any probability distribution is 1
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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.
An area of a normal probability distribution represents?
The number 1. The area of any probability distribution equals 1.
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.
How is probability related to the area under the normal curve?
The Normal curve is a graph of the probability density function of the standard normal distribution and, as is the case with any continuous random variable (RV), the probability that the RV takes a value in a given range is given by the integral of the function between the two limits. In other words, it is the area under the curve between those two values.
Is the total shape of a bell curve greater than 1?
It is assumed that by "shape" you mean "area". The quick answer is yes, probably. The "Bell curve" is called a Gaussian function (see related link). The area under a Gaussian is not necessarily 1; it can be anything. However, if you're talking about probability, where the probability distribution is in the same of a Gaussian, then the area under the curve must be exactly 1. This isn't however, because it is a bell curve, but because it's a probability distribution. The area under any probability distribution must always be exactly 1, or it isn't a valid distribution. The proper term for the total area under any curve f(x) is the integral from negative infinity to infinity of f(x) dx
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.
An area of a normal probability distribution represents?
The number 1. The area of any probability distribution equals 1.
What is the probability associated with the area to the right of the mean in a normal distribution?
50%
What does area have to do with probability?
A normalized probability distribution curve has an area under the curve of 1.Note: I said "normalized", not "normal". Do not confuse the terms.
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 within a continuous probability distribution is equal to 1?
Yes.
Why does a researcher want to go from a normal distribution to a standard normal distribution?
A researcher wants to go from a normal distribution to a standard normal distribution because the latter allows him/her to make the correspondence between the area and the probability. Though events in the real world rarely follow a standard normal distribution, z-scores are convenient calculations of area that can be used with any/all normal distributions. Meaning: once a researcher has translated raw data into a standard normal distribution (z-score), he/she can then find its associated probability.
How do you find the area of a normal distribution?
The area under a normal distribution is one since, by definition, the sum of any series of probabilities is one and, therefore, the integral (or area under the curve) of any probability distribution from negative infinity to infinity is one. However, if you take an interval of a normal distribution, its area can be anywhere between 0 and 1.
What value of Z from the standard normal distribution table has an area to the left probability equal to 0.0764?
-1.43 (approx)
What value of Z from the standard normal distribution has an area probability to the right equal to 0.0643?
z = 1.52 (approx)
Is total area under a normal distribution finite?
Yes, and is equal to 1. This is true for normal distribution using any mean and variance.
Are these true of normal probability distribution IIt is symmetric about the mean TTotal area under the normal distribution curve is equal to 1 DDistribution is totally described by two quantities?
Yes, it is true; and the 2 quantities that describe a normal distribution are mean and standard deviation.
