Normal distribution, Mathematics

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.

Posted Date: 9/15/2012 1:56:23 AM | Location : United States

Related Discussions:- Normal distribution, Assignment Help, Ask Question on Normal distribution, Get Answer, Expert's Help, Normal distribution Discussions

Write discussion on Normal distribution
Your posts are moderated
Related Questions
hi,i want know about Assignment work..

AFIGURE THIS OUT(3) (14) (17) (20) (25)= 8 WHAT ARE THE PROCEDURES (-)(+)(x)(div) BETWEEN EACH NUMBER TO COME UP WITH 8 ?sk question #Minimum 100 words accepted#

HOW MANY number laying between 100 and 1000 can be formed with 0,1,2,3,4,5 and also divisible by 5 with distinct digit

Laws of Set Algebra From the given Venn diagram where T is the universal set and A its subset that we can deduce a number of laws as: i. A υ Ø = A ii. A υ T = T

What do you need to multiply 30 by to get 1500? This will give you the top edge length of the rectangle. Can you then figure out what must go below the 30 in order to get the area

Equivalent or Equal sets Two sets C and D are said to be equal whether every member of set C belongs to D and every member of set D belongs also to C.

Thus, just why do we care regarding direction fields? Two nice pieces of information are there which can be readily determined from the direction field for a differential equation.

Find the probability of drawing a diamond card in each of the two consecutive draws from a well shuffled pack of cards, if the card drawn is not replaced after the first draw

Show that 571 is a prime number. Ans:    Let x=571⇒√x=√571 Now 571 lies between the perfect squares of  (23)2 and (24)2 Prime numbers less than 24 are 2,3,5,7,11,13,17,1

When three quantities a, b and c are in G.P., then the geometric mean "b" is calculated as follows. Since these quantities are in G.P., the r