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

What fraction of water flows out, A conical vessel of radius 6cm and height...

A conical vessel of radius 6cm and height 8cm is completely filled with water. A sphere is lowered into the water and its size is such that when it touches the sides, it is just im

Vijay, how to solve trignometric equations more easier?

how to solve trignometric equations more easier?

first and third quartiles, From the data given below calculate the value o...

From the data given below calculate the value of first and third quartiles, second and ninth deciles and forty-fifth and fifty-seventh percentiles.

Properties of cross product - vector, Properties of Cross product If u,...

Properties of Cross product If u, v and w are vectors and c is a number then u → * v → = -v → * w →                                                       (cu → ) * v → =

Alcohol solution (mixture), Nora works at a laboratory as a chemist . she w...

Nora works at a laboratory as a chemist . she was told to prepare 100L of 25% alcohol solution. she has on hand of a 15% percent alcohol solution and a 40% alcohol solution which s

Algebra problem solving , A rectangles lenth is (x+4) and width is (x+3).By...

A rectangles lenth is (x+4) and width is (x+3).By adding binomials give its perimiter

Determine the volume of the object, A rectangular container is 15 cm wide a...

A rectangular container is 15 cm wide and 5 cm long, and contains water to a depth of 8 cm. An object is placed in the water and the water rises 2.3 cm. Determine the volume of the

Economics, A mortgage lender seeks to maximize the expected value of its po...

A mortgage lender seeks to maximize the expected value of its portfolio. The portfolio, of course, is the sum of all of the mortgages in it, so no generality is lost by examining t

Translating word phrases into algebraic expressions, How do I solve this pr...

How do I solve this problem: Manuel is a cross-country runner for his school’s team. He jogged along the perimeter of a rectangular field at his school. The track is a rectangle th

Which state sold corsica to france in 1768, By which of those ancient civil...

By which of those ancient civilizations was Machu Pichu built? The Aztecs The Egyptians The Mayas The Incas Which state sold Corsica to France in 1768? - Not answered Genoa Veni

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