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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
Is normal distribution symmetrical?
Yes. By definition. A normal distribution has a bell-shaped density curve described by its mean and standard deviation. The density curve is symmetrical(i.e., an exact reflection of form on opposite sides of a dividing line), and centered about (divided by) its mean, with its spread (width) determined by its standard deviation. Additionally, the mean, median, and mode of the distribution are equal and located at the peak (i.e., height of the curve).
Why if a probability distribution curve is bell shaped why is this a normal distribution?
A bell shaped probability distribution curve is NOT necessarily a normal distribution.
Normal curve is the meaning of standard normal distribution?
No, the normal curve is not the meaning of the Normal distribution: it is one way of representing it.
What is the math shape when it looks like a bow?
It could be a Gaussian curve (Normal distribution) rotated through a right angle.It could be a Gaussian curve (Normal distribution) rotated through a right angle.It could be a Gaussian curve (Normal distribution) rotated through a right angle.It could be a Gaussian curve (Normal distribution) rotated through a right angle.
Which normal distribution is also the standard normal curve?
The normal distribution would be a standard normal distribution if it had a mean of 0 and standard deviation of 1.
Why the normal distribution curve have extremes is opened?
Because the domain of the normal distribution is infinite - in both directions.
Is it true that a normal distribution curve is symmetric about the mean?
yup, it's a bell curve
What musical object is often used to describe the curve normal distribution produces?
A bell curve describes the graphed curve that normal distribution produces for a set of data. The curve slopes upward before returning downward after the point of the mean.
Why is the normal curve significant?
Your question makes no sense. Significant is a word related to tests. The normal curve is a distribution, not a test.
Why two tail of normal distribution do not touch the horizontal axis?
The domain of the Normal distribution is the whole of the real line. As a result the horizontal axis is asymptotic to the Normal distribution curve. The curve gets closer and closer to the axis but never, ever reaches it.
What uses rectangles to show frequency distribution?
normal curve
Is the a normal distribution curve negative or positive?
Neither. It is symmetrical.
What are the characteristics a standard normal probability distribution?
I apologize my question should have read what are the characteristics of a standard normal probability distribution? Thank you
