Normal distribution, Mathematics

Assignment Help:

Normal Distribution

Figure 1

1015_normal distribution.png

The normal distribution reflects the various values taken by many real life variables like the heights and weights of people or the marks of students in a large class. In all these cases a large number of observations are found to be clustered around the mean value m and their frequency drops sharply as we move away from the mean in either direction. For example, if the mean height of an adult in a city is 6 feet then a large number of adults will have heights around 6 feet. Relatively a few adults will have heights of 5 feet or 7 feet.

Further, if we draw samples of size n (where n is a fixed number over 30) from any population, then the sample mean 89_computation of covariance ungrouped data2.png   will be (approximately) normally distributed with a mean equal to m i.e. the mean of the population.

The characteristics of normal probability distribution with reference to the above figure are

  1. The curve has a single peak; thus it is unimodal.

  2. The mean of a normally distributed population lies at the center of its normal curve.

  3. Because of the symmetry of the normal probability distribution, the median and the mode of the distribution are also at the center.

  4. The two tails of the normal probability distribution extend indefinitely and never touch the horizontal axis.

If s is the standard deviation of the normal distribution, 80% of the observation will be in the interval m -1.28s to m + 1.28s.

Figure 2

375_normal distribution1.png

95% of the observations will be in the interval m - 1.96s to m + 1.96s.

Figure 3

2353_normal distribution2.png

98% of the observations will lie in the interval m - 2.33 s to m + 2.33 s.

Figure 4

342_normal distribution3.png

 

 

Standard Normal Distribution

The Standard Normal Distribution is a normal distribution with a mean m = 0 and a standard deviation s = 1. The observation values in a standard normal distribution are denoted by the letter Z.


Related Discussions:- Normal distribution

Linear programming , use the simplex method to solve the following lp probl...

use the simplex method to solve the following lp problem. max z = 107x1 + x2 + 2x3 subject to 14x1 + x2 - 6x3 + 3x4 = 7 16x1 + x2 - 6x3 3x1 - x2 - x3 x1,x2,x3,x4 > = 0

Prove sum of squares any two sides equal twice square, Prove that in any tr...

Prove that in any triangle the sum of the squares of any two sides is equal to twice the square of half of the third side together with twice the square of the median, which bisect

find the present age, 5 years however, a man's age will be 3times his son'...

5 years however, a man's age will be 3times his son's age and 5 years ago, he was 7 times as old as his son.    Find their present ages.

H, 6987+746-212*7665

6987+746-212*7665

Calculate probability, The following table contains some information about...

The following table contains some information about the model used. Assume the probabilities given by the model are those of being a good writer. Variable

SYSTEMS OF ODE, Problem 1 Let ~x0 = A~x and y 0 = B~y be two 2  2 linear s...

Problem 1 Let ~x0 = A~x and y 0 = B~y be two 2  2 linear systems of ODE. (1) Suppose that A and B have the same purely imaginary eigenvalues. Prove that these systems are topologi

Calculate the net amount and distance, 1. A train on the Bay Area Rapid Tra...

1. A train on the Bay Area Rapid Transit system has the ability to accelerate to 80 miles/hour in half a minute. A.   Express the acceleration in miles per hour per minute. B

Permatuation and combination problem, A,B,C are natural numbers and are in ...

A,B,C are natural numbers and are in arithmetic progressions and a+b+c=21.then find the possible values for a,b,c Solution) a+b+c=21 a+c=2b 3b=21 b=7 a can be 1,2,3,4,5,6 c c

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd