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Q: What is the percentile rank of the score 20 in a unit normal distribution that has a population mean of 21 and a variance of 4?

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A normal distribution can have any value for its mean and any positive value for its variance. A standard normal distribution has mean 0 and variance 1.

The normal distribution can have any real number as mean and any positive number as variance. The mean of the standard normal distribution is 0 and its variance is 1.

le standard normal distribution is a normal distribution who has mean 0 and variance 1

The standard normal distribution is a normal distribution with mean 0 and variance 1.

Yes, the mean (and median and mode) is the 50th percentile of any normal distribution.

The standard normal distribution is a special case of the normal distribution. The standard normal has mean 0 and variance 1.

Actually the normal distribution is the sub form of Gaussian distribution.Gaussian distribution have 2 parameters, mean and variance.When there is zero mean and unit variance the Gaussian distribution becomes normal other wise it is pronounced as Gaussian.Wrong! The standard normal distribution has mean 0 and variance 1, but a normal distribution is the same as the Gaussiand, and can have any mean and variance. Google stackexcange "what-is-the-difference-between-a-normal-and-a-gaussian-distribution"

The mean and variance.

The standard normal distribution has mean 0 and variance 1. It is not clear what 0.62 has to do with the distribution.

A Gaussian distribution is the "official" term for the Normal distribution. This is a probability density function, of the exponential family, defined by the two parameters, its mean and variance. A population is said to be normally distributed if the values that a variable of interest can take have a normal or Gaussian distribution within that population.

A mathematical definition of a standard normal distribution is given in the related link. A standard normal distribution is a normal distribution with a mean of 0 and a variance of 1.

The standard normal distribution or the Gaussian distribution with mean 0 and variance 1.

true

The mean is 0 and the variance is 1. This need not be the case in any other Normal (Gaussian) distribution.

Yes, and is equal to 1. This is true for normal distribution using any mean and variance.

z-scores are distributed according to the standard normal distribution. That is, with the parameters: mean 0 and variance 1.

When we discuss a sample drawn from a population, the larger the sample, or the large the number of repetitions of the event, the more certain we are of the mean value. So, when the normal distribution is considered the sampling distribution of the mean, then more repetitions lead to smaller values of the variance of the distribution.

The variance is always positive. The variance is not directly related to the sign (nor magnitude) of the mean.

The mean must be 0 and the variance must be 1.

it doesn't exist.

No. The variance of any distribution is the sum of the squares of the deviation from the mean. Since the square of the deviation is essentially the square of the absolute value of the deviation, that means the variance is always positive, be the distribution normal, poisson, or other.

Yes. Normal (or Gaussian) distribution are parametric distributions and they are defined by two parameters: the mean and the variance (square of standard deviation). Each pair of these parameters gives rise to a different normal distribution. However, they can all be "re-parametrised" to the standard normal distribution using z-transformations. The standard normal distribution has mean 0 and variance 1.

It depends on the underlying distribution. If Gaussian (standrad normal) then the percentile is 77.

Answer: 0 The z score is the value of the random variable associated with the standardized normal distribution (mean = 0, standard deviation =1). Now, the median and the mean of a normal distribution are the same. The 50 percentile z score = the median = mean = 0.

Only one. A normal, or Gaussian distribution is completely defined by its mean and variance. The standard normal has mean = 0 and variance = 1. There is no other parameter, so no other source of variability.

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