A standard normal distribution has a mean of zero and a standard deviation of 1. A normal distribution can have any real number as a mean and the standard deviation must be greater than zero.
No, they are rarely the same.
Because the standard deviation is one of the two parameters (the other being the mean) which define the Normal curve. The mean defines the location and the standard deviation defines its shape.
Smaller
If the Z-Score corresponds to the standard deviation, then the distribution is "normal", or Gaussian.
The standard normal curve is symmetrical.
Mean = 0 Standard Deviation = 1
Yes. By definition. A normal distribution has a bell-shaped density curve described by its mean and standard deviation. The density curve is symmetrical(i.e., an exact reflection of form on opposite sides of a dividing line), and centered about (divided by) its mean, with its spread (width) determined by its standard deviation. Additionally, the mean, median, and mode of the distribution are equal and located at the peak (i.e., height of the curve).
1
The distance between the middle and the inflection point is the standard deviation.
A standard normal distribution has a mean of zero and a standard deviation of 1. A normal distribution can have any real number as a mean and the standard deviation must be greater than zero.
It is 15 points.
No, they are rarely the same.
The normal distribution would be a standard normal distribution if it had a mean of 0 and standard deviation of 1.
Because the standard deviation is one of the two parameters (the other being the mean) which define the Normal curve. The mean defines the location and the standard deviation defines its shape.
Smaller
The mean must be 0 and the standard deviation must be 1. Use the formula: z = (x - mu)/sigma