Intuitively, a standard deviation is a change from the expected value.
For the question you asked, this means that the change in the "results" doesn't exist, which doesn't really happen. If the standard deviation is 0, then it's impossible to perform the test! This shows that it's impossible to compute the probability with the "null" standard deviation from this form:
z = (x - µ)/σ
If σ = 0, then the probability doesn't exist.
Mean 0, standard deviation 1.
Mean = 0 Standard Deviation = 1
No.
a is true.
If all four numbers are the same, there is no standard deviation. The mean will be equal to all 4 numbers, resulting in a 0 standard deviation. Ex) 5,5,5,5
Mean 0, standard deviation 1.
Mean = 0 Standard Deviation = 1
No.
It is not. And that is because the mean deviation of ANY variable is 0 and you cannot divide by 0.
standard normal
The standard deviation is 0.
The standard deviation for a single observation is 0.
a is true.
The smaller the standard deviation, the closer together the data is. A standard deviation of 0 tells you that every number is the same.
A standard deviation of zero means that all the data points are the same value.
Standard deviation doesn't have to be between 0 and 1.
Standard deviation of a single event is 0.