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Q: What requirements are necessary for a normal probability distribution to be a standard normal probability distribution?

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no

The mean and standard deviation do not, by themselves, provide enough information to calculate probability. You also need to know the distribution of the variable in question.

A researcher wants to go from a normal distribution to a standard normal distribution because the latter allows him/her to make the correspondence between the area and the probability. Though events in the real world rarely follow a standard normal distribution, z-scores are convenient calculations of area that can be used with any/all normal distributions. Meaning: once a researcher has translated raw data into a standard normal distribution (z-score), he/she can then find its associated probability.

The Poisson distribution is a discrete distribution, with random variable k, related to the number events. The discrete probability function (probability mass function) is given as: f(k; L) where L (lambda) is the mean and square root of lambda is the standard deviation, as given in the link below: http://en.wikipedia.org/wiki/Poisson_distribution

Because, whatever the underlying distribution, as more and more samples are taken from ANY population, the average of those samples will have a standard normal distribution whose mean will be their average. The normal (or Gaussian) distribution is symmetric and so its mean lies at the centre of the probability distribution.

Related questions

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

Yes.

I apologize my question should have read what are the characteristics of a standard normal probability distribution? Thank you

with mean and standard deviation . Once standardized, , the test statistic follows Standard Normal Probability Distribution.

When its probability distribution the standard normal distribution.

no

Zero.

with mean of and standard deviation of 1.

a mean of 1 and any standard deviation

It is the Standard Normal distribution.

The normal distribution and the t-distribution are both symmetric bell-shaped continuous probability distribution functions. The t-distribution has heavier tails: the probability of observations further from the mean is greater than for the normal distribution. There are other differences in terms of when it is appropriate to use them. Finally, the standard normal distribution is a special case of a normal distribution such that the mean is 0 and the standard deviation is 1.

probability is 43.3%

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