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Characteristics of a Normal Distribution
1) 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) Unimodal
5) Mean = Median = Mode
6) Symmetrical with respect to the mean
That is, 50% of the area (data) under the curve lies to the left of
the mean and 50% of the area (data) under the curve lies
to the right of the mean.
7) (a) 68% of the area (data) under the curve is within one
standard deviation of the mean
(b) 95% of the area (data) under the curve is within two
standard deviations of the mean
(c) 99.7% of the area (data) under the curve is within three
standard deviations of the mean
8) The total area under the normal curve is equal to 1.
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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.
What requirements are necessary for a normal probability distribution to be a standard normal probability distribution?
The normal distribution, also known as the Gaussian distribution, has a familiar "bell curve" shape and approximates many different naturally occurring distributions over real numbers.
What is the shape of a normal distribution?
It is a symmetrical, "bell-shaped" curve. The tails are infinitely long.
What must be done to a normal curve to make it into a standard normal distribution curve?
The mean must be 0 and the standard deviation must be 1. Use the formula: z = (x - mu)/sigma
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.
