Nothing particular, since z is symmetric about zero. Half the time z is negative.
The answer will depend on the underlying distribution for the variable. You may not simply assume that the distribution is normal.
If a random variable X has a Normal distribution with mean m and standard deviation s, then z = (X - m)/s has a Standard Normal distribution. That is, Z has a Normal distribution with mean 0 and standard deviation 1. Probabilities for a general Normal distribution are extremely difficult to obtain but values for the Standard Normal have been calculated numerically and are widely tabulated. The z-transformation is, therefore, used to evaluate probabilities for Normally distributed random variables.
If you have a variable X that is normally distributed with mean m and variance s2 then the z-score, Z = (X - m)/s.Z has a standard Normal distribution.
The standard normal distribution is a special case of the normal distribution. The standard normal has mean 0 and variance 1.
The area under the standard normal curve is 1.
It is the Standard normal variable.
Use the context: if the variable should be greater than the mean then z is positive and if less than the mean, it should be negative.
It is 0.5
About half the time.
None.z-scores are linear transformations that are used to convert an "ordinary" Normal variable - with mean, m, and standard deviation, s, to a normal variable with mean = 0 and st dev = 1 : the Standard Normal distribution.
If a variable X, is distributed Normally with mean m and standard deviation s thenZ = (X - m)/s has a standard normal distribution.
An ordinary variable is standardised by taking a linear transformation of it such that the new variable has standard properties. For example, if X is a Gaussian (Normal) variable with mean mu and standard deviation sigma, then Z = (X - mu)/sigma has a Normal distribution with mean 0 and SD = 1: it has been standardised.
0.636 approx.
It is 0.1587
Yes, to approximately standard normal.If the random variable X is approximately normal with mean m and standard deviation s, then(X - m)/sis approximately standard normal.
The z-score is used to convert a variable with a Gaussian [Normal] distribution with mean m and standard error s to a variable with a standard normal distribution. Since the latter is tabulated, the probability of an outcome as extreme or more compared to the one observed is easily obtained.
It is 1.17