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.
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.
a mean of 1 and any standard deviation
The mean must be 0 and the variance must be 1.
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 normal distribution, also known as the Gaussian distribution, has a familiar "bell curve" shape and approximates many different naturally occurring distributions over real numbers.
No. Normal distribution is a continuous probability.