There are no benefits in doing something that cannot be done. The standard normal distribution is not transformed to the standard distribution because the latter does not exist.
For a normal probability distribution to be considered a standard normal probability distribution, it must have a mean of 0 and a standard deviation of 1. This standardization allows for the use of z-scores, which represent the number of standard deviations a data point is from the mean. Any normal distribution can be transformed into a standard normal distribution through the process of standardization.
The standard deviation in a standard normal distribution is 1.
The standard deviation in a standard normal distribution is 1.
The standard normal distribution is a special case normal distribution, which has a mean of zero and a standard deviation of one.
There are no benefits in doing something that cannot be done. The standard normal distribution is not transformed to the standard distribution because the latter does not exist.
You may transform a normal distribution curve, with, f(x), distributed normally, with mean mu, and standard deviation s, into a standard normal distribution f(z), with mu=0 and s=1, using this transform: z = (x- mu)/s
The standard normal distribution has a mean of 0 and a standard deviation of 1.
The standard normal distribution is a normal distribution with mean 0 and variance 1.
The normal distribution would be a standard normal distribution if it had a mean of 0 and standard deviation of 1.
The standard deviation in a standard normal distribution is 1.
The standard deviation in a standard normal distribution is 1.
The standard normal distribution is a special case of the normal distribution. The standard normal has mean 0 and variance 1.
A mathematical definition of a standard normal distribution is given in the related link. A standard normal distribution is a normal distribution with a mean of 0 and a variance of 1.
The standard normal distribution is a special case normal distribution, which has a mean of zero and a standard deviation of one.
The normal distribution is very difficult to work with: the probability density function is not simple [I suspect that only a few mathematics graduates from university would be able to integrate it!]. The standard normal has been tabulated in considerable detail and so, if the normal is transformed to the standard normal, most of the analyses, hypothesis testing, confidence intervals and so on can be found by looking up tables.
Yes, the normal distribution, standard or not is always continuous.