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Q: What are the characteristics a standard normal probability distribution?

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When its probability distribution the standard normal distribution.

Yes.

a mean of 1 and any standard deviation

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

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When its probability distribution the standard normal distribution.

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

Yes.

with mean of and standard deviation of 1.

Zero.

It is the Standard Normal distribution.

a mean of 1 and any standard deviation

No. Normal distribution is a continuous probability.

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.

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

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.

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.

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