Normal Distribution Data Set

Gaussian distribution is called as normal distribution. The normal distribution of the data is defined by two parameters mean (m) or average and standard deviation (s). A theoretical frequency distribution of the data is a set of variable; normally the data mean values are represented by bell-shaped curve symmetrical. In this article we shall discuss about normal distribution of data set example problem.

Normal distribution data set example problem:

Normal distribution:


X value < mean value = 0.5 - Z value

X value > mean value = 0.5+Z value

X value = mean value = 0.5

Z value = (X-m) / s

where,

m = Mean.

s = Standard Deviation.

X = Normal Random Variable

Example:

Let X be a normal random variable with mean value (m) 118 and standard deviation (s) is 5 find the P(X<108 p="">
Step 1:

For the given X value =108

Z = (108-118)/5

= 1

Step 2:

Find out the value of 1 in Z table (The value of Z table 1 = 0.3413)

Z = 1 = 0.3413

Step 3:

Here the value of X is less than mean so

P(X) = 0.5 - 0.3413 = 0.1587

Normal distribution is 0.1587

Example:

Let X be a normal random variable with mean value (m) 108 and standard deviation (s) is 6 find the P(X<112 p="">
Step 1:

For the given X value =112

Z = `(112-106)/6 ` = `4/6`

= 0.6

Step 2:

Find out the value of 0.6 in Z table (The value of Z table 0.6 = 0.2257)

Z = 0.6 = 0.2257
Step 3:

Here the value of X is greater than mean so

P(X) = 0.5 + 0.2257= 0.7257

Normal distribution is 0.7257

Normal distribution data set practice problem

Problem:

Let X be a normal random variable with mean value (m) 112 and standard deviation (s) is 6 find the P(X<106 p="">
Answer:

Normal distribution is 0.1587

Problem:

Let X be a normal random variable with mean value (m) 106 and standard deviation (s) is 5 find the P(X<110 p="">
Answer:

Normal distribution is 0.78819