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
who discovered unitary meathod


a math problem that involves the numbers $112 for 8 hours

Homework is worth 10% of my grade, quizzes are worth 30%, and tests are worth 40%. I have 15 grades in the homework section, they''re all 100''s. I have 2 grades in the quiz sectio

how do you solve expressions

Discontinuous Integrand- Integration Techniques Here now we need to look at the second type of improper integrals that we will be looking at in this section.  These are integr

Example 1: Multiply 432 by 8. Solution:        432 ×        8 --------------       3,456 In multiplying the multiplier in the units column to the multiplica


how long would it take if a submarine if it goes 3 feet per minute to get to 20000 answer

If i worked 7 1/3 hours and planted 11 trees how many hours did it take to plant each tree?