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When we say a distribution is normal, we refer to a statistical distribution that follows a bell-shaped curve, characterized by its symmetry about the mean. In a normal distribution, approximately 68% of the data falls within one standard deviation of the mean, 95% within two standard deviations, and 99.7% within three standard deviations. This distribution is defined by its mean and standard deviation, and it is widely used in statistics due to the Central Limit Theorem, which states that the sum of many independent random variables tends toward a normal distribution, regardless of the original distribution.
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What does it mean when you say a variable is normally distributed?
It means that the probability distribution function of the variable is the Gaussian or normal distribution.
Why is it correct to say a normal disstrubtion and the standard normal distribution?
A normal distribution refers to a continuous probability distribution that is symmetrical and characterized by its mean and standard deviation. In contrast, the standard normal distribution is a specific case of the normal distribution where the mean is 0 and the standard deviation is 1. This standardization allows for easier comparison and calculation of probabilities using z-scores, which represent the number of standard deviations a data point is from the mean. Thus, while all standard normal distributions are normal, not all normal distributions are standard.
Is normal distribution hypothetical?
The normal distribution is a theory, which works in practice (with a large enough sample). E.g if you were to plot the height of everyone in the country, you should end up with a normal distribution. Hence it is not usually considered hypothetical, in the same way that, say, imaginary numbers are hypothetical.
Does a normal probability distribution include a bimodal distribution?
No, the normal distribution is strictly unimodal.
Is normal distribution also a probability distribution?
Yes. When we refer to the normal distribution, we are referring to a probability distribution. When we specify the equation of a continuous distribution, such as the normal distribution, we refer to the equation as a probability density function.
When can you say the distribution is considered normal?
When its probability distribution the standard normal distribution.
What does it mean when you say a variable is normally distributed?
It means that the probability distribution function of the variable is the Gaussian or normal distribution.
What is the difference between a normal distribution and the standard normal distribution?
The standard normal distribution is a normal distribution with mean 0 and variance 1.
What is the difference of a normal distribution and a stardard normal distribution?
The standard normal distribution is a special case of the normal distribution. The standard normal has mean 0 and variance 1.
Is continuous distribution normal distribution?
le standard normal distribution is a normal distribution who has mean 0 and variance 1
Is normal distribution hypothetical?
The normal distribution is a theory, which works in practice (with a large enough sample). E.g if you were to plot the height of everyone in the country, you should end up with a normal distribution. Hence it is not usually considered hypothetical, in the same way that, say, imaginary numbers are hypothetical.
Does a normal probability distribution include a bimodal distribution?
No, the normal distribution is strictly unimodal.
Is the normal distribution infinite?
The domain of the normal distribution is infinite.
How does standard normal distribution differ from normal distribution?
The standard normal distribution has a mean of 0 and a standard deviation of 1.
What is symmetrical normal distribution?
The Normal distribution is, by definition, symmetric. There is no other kind of Normal distribution, so the adjective is not used.
Is normal distribution also a probability distribution?
Yes. When we refer to the normal distribution, we are referring to a probability distribution. When we specify the equation of a continuous distribution, such as the normal distribution, we refer to the equation as a probability density function.
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.
