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with mean and standard deviation . Once standardized, , the test statistic follows Standard Normal Probability Distribution.
with mean of and standard deviation of 1.
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.
Only the mean, because a normal distribution has a standard deviation equal to the square root of the mean.
The mean of a standard normal distribution is 0.