# The Standard Normal Distribution

The standard normal distribution table gives the probability of a regularly distributed random variable Z, whose mean is equivalent to 0 and difference equal to 1, is not exactly or equal to z. Normal distribution is a persistent probability distribution. It is also called Gaussian distribution. It is pertinent for positive estimations of z only.

Standard normal distribution table is utilized to ascertain the region under the bend( f(z)) to discover the probability of a specified range of distribution. The normal distribution density function f(z) is called the Bell Curve since it’s shape looks like a bell.

What it means is that on the off chance that you need to discover the probability of value being not exactly or more than a fixed positive z value. You can discover it by finding it on the table. This is known as area Φ.

Diagrammatically, the probability of Z not exactly “a” being Φ(a), figured from the standard normal distribution table, is demonstrated as follows:

P(Z < –a)

As specified over, the standard normal distribution table just gives the probability to values not exactly a positive z value (i.e., z values on the right hand side of the mean). So how would we ascertain the probability beneath a negative z value (as outlined below)?

P(Z > a)

The probability of P(Z > a) is 1 – Φ(a). To understand the reasoning behind this look at the illustration below:

You know Φ(a) and you realize that the total area under the standard normal curve is 1 so by

numerical conclusion: P(Z > an) is: 1 Φ(

a).

P(Z > –a)

The probability of P(Z > –a) is P(a), which is Φ(a). To comprehend this, we have to value the symmetry of the standard normal distribution curve. We are attempting to discover the region

Below:If this area is in the region we need.

Notice this is the same size area as the area we are searching for, just we know this area, as we can get it straight from the standard normal distribution table: it is

P(Z < a). In this way, the P(Z > –a) is P(Z < a), which is Φ(a).

Probability between z values

You are wanting to solve the following: