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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.
Does a probability histogram follow the normal curve?
Not necessarily.
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 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 shape would the probability distribution have for completely uncertain returns?
the variance is infinitely large and in the extreme case the probability distribution curve will simply be a horizontal line
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.
Does a probability histogram follow the normal curve?
Not necessarily.
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 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.
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.
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 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 probability of one dice creating a bell shape curve?
The probability of getting the exact shape of the Gaussian bell shaped curve is 0. And that is true even if you use a billion dice. The curve from repeated throws of one die, or many dice will approximate the Gaussian curve and the approximation will get better as the number of trails increases.However, the Gaussian curve extends to infinity in both direction and there is a very small but non-zero probability associated with these extreme values. You will not get an outcome that is infinite!
What shape would the probability distribution have for completely uncertain returns?
the variance is infinitely large and in the extreme case the probability distribution curve will simply be a horizontal line
What percentage of normally distributed scores lie under the normal curve?
100%. And that is true for any probability distribution.
How would you describe the shape of a normal curve?
Bell-shaped, unimodal, symmetric
Would you ever get a normal curve bell shape that is perfect?
Only in theory.
