Chapter 3. The Normal Distributions
Chapter 3. The Normal Distributions
1
Chapter 3. The Normal Distributions
Density Curves
Definition. A (probability) density curve is a curve that
? is always on or above the horizontal axis, and
? has area exactly 1 underneath it (that is, the area between
the curve and the x?axis).
A density curve describes the overall pattern of a distribution.
The area under the curve and above any range of values is the
proportion of all observations that fall in that range.
Example. Exercise 3.1 page 67.
Chapter 3. The Normal Distributions
2
Describing Density Curves
Definition. The median of a density curve is the equalareas point, the point that divides the area under the curve
in half. That is, half of the area under the curve is to the
left of the median and the remaining half of the area is to its
right. The mean of a density curve is the balance point, at
which the curve would balance if made of solid material. The
median and mean are the same for a symmetric density curve.
Figures 3.4(a) and 3.4(b) page 68.
Figure 3.5 page 68.
Chapter 3. The Normal Distributions
3
Note. The usual notation for the mean of an idealized distribution is ? (mu). The standard deviation of a density curve
is denoted ¦Ò (sigma).
Example. Exercise 3.4 page 69.
Chapter 3. The Normal Distributions
4
Normal Distributions
Note. A VERY common class of density curves is the normal
distributions. These curves are symmetric, single-peaked,
and bell-shaped. All normal distributions have similar shapes
and are determined solely by their mean ? and standard deviation ¦Ò. The points at which the curves change concavity are
located a distance ¦Ò on either side of ?. We will use the area
under these curves to represent a percentage of observations.
(These areas correspond to integrals, for those of you with
some experience with calculus.)
Figure 3.8 page 70.
Chapter 3. The Normal Distributions
5
Note. The text mentions three reasons we are interested in
normal distributions:
1. Normal distributions are good descriptions for some distributions of real data. Examples include test scores and
characteristics of biological populations (such as height or
weight).
2. Normal distributions are good approximations to the results of many kinds of chance outcomes. An example is
the proportion of heads in a repeatedly tossed coin experiment.
3. Many statistical inference procedures based on normal distributions work well for other roughly symmetric distributions.
................
................
In order to avoid copyright disputes, this page is only a partial summary.
To fulfill the demand for quickly locating and searching documents.
It is intelligent file search solution for home and business.
Related download
- crp 272 the normal distribution iowa state university
- examples of continuous probability distributions
- the normal distribution
- mbbs stage i notes on the normal distribution samples and
- 3 the multivariate normal distribution
- random variables and probability distributions
- 10 geometric distribution examples
- history of the normal distribution university of utah
- continuous distributions normal distribution in
- important probability distributions
Related searches
- chapter 3 developmental psychology quizlet
- mcgraw hill algebra1 chapter 3 lesson 8
- chapter 3 psychology quizlet test
- psychology chapter 3 quiz answers
- developmental psychology chapter 3 quizlet
- strategic management chapter 3 quizlet
- psychology chapter 3 exam
- psychology chapter 3 test questions
- the outsiders chapter 3 pdf
- the outsiders chapter 3 questions
- the outsiders chapter 3 summary
- z score standard normal distributions calculator