Normal Sum Distribution

Introduction to normal sum distribution:

Let us see about normal sum distribution,

The normal distribution is also known as the normal probability distribution, happens to be the mainly helpful theoretical distribution for continuous variables. A lot of statistical data sum regarding business and economic problems are display in the type of normal sum distribution.In fact normal distribution is known as the ‘corner stone’ of  Modern statistics.Just like the Poisson distribution, the normal sum  distribution  may also be regarded as a limiting case of binomial distribution.

Definition of Normal Sum Distribution:

Let we see about definition of normal sum distribution,

A variable X is told that a normal distribution with parameter µ and s (or µ and s2) if the probability function is,

Here, Z =(X – µ) s

Constants of Normal distribution:

Mean = µ

Variance = s2

Standard deviation = s

The graph sum of the normal curve is shown below,

The distribution with µ = 0 and s2 = 1 is known as the standard normal distribution.

Understanding problem solving with proportions is always challenging for me but thanks to all math help websites to help me out.

Normal Sum Distribution-example Problems:

1) If X is normally distributed having mean 7 and standard deviation 6 find. P(0 = X = 10).

Solution :

Given, µ = 7, s = 6

(i) P(0 = X = 10)

We know that Z =(X – µ) / s

When X = 0, Z =(0 – 7) / 6 = -1.16

When X = 10, Z =(10 – 6) / 6 = 4/6 = 0.67

? P(0 = X = 10) = P(-1.2 < Z < 0.67)

= P( 0 < Z < 1.2) + P( 0 < Z < 0 .67) (due to symmetry)

= 0.3849 + 0.258

= 0.516

2) If X is normally distributed having mean 10 and standard deviation 8 find. P(0 = X = 20).

Solution :

Given, µ = 10, s = 8

Find, P(0 = X = 20)

We know that Z =(X – µ) / s

When X = 0, Z =(0 – 10) / 8 = -1.3

When X = 10, Z =(20 – 10) / 8= 10/6 = 1.3

? P(0 = X = 20) = P(-1.3 < Z < 0.3)

= P( 0 < Z < 1.3) + P( 0 < Z < 0 .3) (due to symmetry)

= 0.4032 + 0.4032

= 0.8064