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

The mean value theorem for integrals, The Mean Value Theorem for Integrals ...

The Mean Value Theorem for Integrals If f(x) is a continuous function on [a,b] then here is a number c in [a,b] thus, a ∫ b f(x) dx = f(c)(b -a) Proof Let's begin

Problem Solving, the low temperature in anchorage alaska today was negative...

the low temperature in anchorage alaska today was negative four degrees what is the difference in the two low temperatures

Find the length of the rectangle, Suppose that the width of a rectangle is ...

Suppose that the width of a rectangle is three feet shorter than length and that the perimeter of the rectangle is 84 feet. a)    Set up an equation for the perimeter involving

Lim x, Q. lim x tends to 0 (5 tanx sinx upon x square) here ( ) this bracke...

Q. lim x tends to 0 (5 tanx sinx upon x square) here ( ) this bracket indicates greatest integer function Ans: You can calculate the limit of this function using basic concept of

Find a power series representation for the function, Find a power series re...

Find a power series representation for the subsequent function and find out its interval of convergence. g (x) = 1/1+x 3 Solution What we require to do here is to rela

Launching of a new product, Launching a new product (Blackberry Cube) Analy...

Launching a new product (Blackberry Cube) Analysis (target market) Product features Promotions and advertisement sample design (location)

Solving geometry using algebra, if one side of a square is increased 4 inch...

if one side of a square is increased 4 inches and an adjacement side is multiplied by 4, the perimeter of the resulting rectangle is 3 times the perimeter of the square. find the s

Concepts, what are core concepts of marketing?

what are core concepts of marketing?

Solve 2 ln (x) - ln (1 - x ) = 2 single logarithm, Solve 2 ln (√x) - ln (1 ...

Solve 2 ln (√x) - ln (1 - x ) = 2 . Solution: Firstly get the two logarithms combined in a single logarithm. 2 ln (√x) - ln (x  - l) = 2 ln ((√x) 2 ) ln (1 - x ) = 2

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