Because of the Central Limit Theorem, the mean value of sets of observations is distributed Normally. Irrespective of the underlying distribution of a variable, the distribution of a sum (or mean) of such variables tends towards the Normal distribution. So, for sufficiently large samples, all distributions can be approximated by thye Normal distribution.
One of the consequences is that the distribution has been studied extensively and a lot is known about tests based on it.
No. Normal distribution is a continuous probability.
Yes. When we refer to the normal distribution, we are referring to a probability distribution. When we specify the equation of a continuous distribution, such as the normal distribution, we refer to the equation as a probability density function.
No, the normal distribution is strictly unimodal.
with mean and standard deviation . Once standardized, , the test statistic follows Standard Normal Probability Distribution.
It is the Standard Normal distribution.
No. Normal distribution is a continuous probability.
Yes. When we refer to the normal distribution, we are referring to a probability distribution. When we specify the equation of a continuous distribution, such as the normal distribution, we refer to the equation as a probability density function.
A bell shaped probability distribution curve is NOT necessarily a normal distribution.
When its probability distribution the standard normal distribution.
Normal distribution is the continuous probability distribution defined by the probability density function. While the binomial distribution is discrete.
No, the normal distribution is strictly unimodal.
The total area of any probability distribution is 1
I apologize my question should have read what are the characteristics of a standard normal probability distribution? Thank you
with mean and standard deviation . Once standardized, , the test statistic follows Standard Normal Probability Distribution.
Yes.
If X has any discrete probability distribution then the sum of a number of observations for X will be normal.
The probability density of the standardized normal distribution is described in the related link. It is the same as a normal distribution, but substituted into the equation is mean = 0 and sigma = 1 which simplifies the formula.