Probability of Normal distribution simple and interesting example(PART-3)

In this video explaining third problem of normal distribution. This problem is very simple and this method helps in engineering and science students. Biostatistics: The normal distribution is used to model various biological variables such as height weight and blood pressure which are assumed to follow a normal distribution in a population.

#easymathseasytricks

Joint Probability & Sampling Theory: 18MAT41 & 17MAT41

Probability Distributions: 18MAT41 & 17MAT41

Calculus of Complex Functions: 18MAT41 & 17MAT41

Curve fitting & Statistical Method 18MAT41 17MAT31

LAPLACE TRANSFORM : 18MAT31

Fourier Transforms,Z-transform : 18MAT31 & 17MAT31

Fourier Series: 18MAT31 & 17MAT31

Calculus of Variation & Numerical Methods 18MAT31

Numerical Methods ODE's: 18MAT31 & 17MAT41

COMPLEX NUMBER: 18MATDIP31

Differential Calculus:18MATDIP31

Ordinary differential equation 18MATDIP31,17MATDIP31

Integral Calculus 18MATDIP31,17MATDIP31

Vector differentiation 18MATDIP31,17MATDIP31

Differential Calculus & Partial Differential 18MATDIP31,17MATDIP31

18MATDIP41 Linear Algebra

18MATDIP41 Numerical Methods

18MATDIP41 Higher order ODEs

18MATDIP41 Partial Differential Equations

[claudiamesaaparicio]

Sorry, but i do not get the part when 0.4192 is approximately is 1.4

[riturekha]

Sir I have small doubt is it important to draw diagram for this particular question??

[santhoshbanoth]

Mean and standard deviations direct ga vesaruu eanteeee sir not understand at last step

[ImBlackDragon]

How did Z1 Become -0.5. You can't just take (-) inside the bracket.

[rowdy]

Sir they will provide tables in exam or not

[velagapudinavya]

Sir I have a doubt this problem please help me

[muhammadridhuan]

hey sir, can i get your email to ask you my question?

[megha_]

In a normal distribution, 31% of the items are under 45 and 8% are over 64. Find the mean and...
Question:
In a normal distribution, 31% of the items are under 45 and 8% are over 64.

Find the mean and standard deviation of this distribution. Please show all work.

Standard Normal Distribution:

The special case of normal distribution with mean of zero and variance of unity is known as standard normal distribution. The p-value is obtained from standard normal table. The density function of standard normal distribution is:




Answer and Explanation: 1

Given Information:

Let the random variable X has normal distribution.


The 31% of the items are under 45, that is,


The 8% of the items are over 64, that is,


The standardized value is obtained by:



Where, {eq}\mu \, \, and\, \, \sigma {/eq} is mean and standard deviation of X, respectively.
is mean and standard deviation of X, respectively.

It is given that,


Further expand the above expression,







It is also given that,


Further expand the above expression,








The mean and standard deviation of the distribution can be obtained as:

From equations (1) and (2),



Therefore, the standard deviation of the distribution is 9.995.

Substitute the value of standard deviation in equation (1) to get the mean,



Therefore, the mean of the distribution is 45.494 .wrong answer