The Normal Distributions and Sampling Distributions - Sections 5.5, 6.5 & 6
The Normal Distributions and Sampling Distributions
Sections 5.5, 6.5 & 6.6
Cathy Poliak, Ph.D.
cathy@math.uh.edu
Office in Fleming 11c
Department of Mathematics
University of Houston
Lecture 8 - 3339
Cathy Poliak, Ph.D. cathy@math.uh.edu Office in FlemingSections
11c (Department
5.5, 6.5 & of
6.6Mathematics University of Houston
Lecture )8 - 3339
1 / 78
Outline
1
Normal Distribution
2
The Empirical Rule
3
The Standard Normal Distribution
4
Using the z-table
5
Inverse Normal
6
Approximating the Binomial Distribution
7
Sums of Random Variables
8
Sampling Distributions
9
Sampling Distribution of X?
10
Finding Probabilities for X?
11
Proportions
12
Sampling Distribution of p?
Cathy Poliak, Ph.D. cathy@math.uh.edu Office in FlemingSections
11c (Department
5.5, 6.5 & of
6.6Mathematics University of Houston
Lecture )8 - 3339
2 / 78
Definition of a Density Function
A density function is a nonnegative function f defined of the set
of real numbers such that:
Z
f (x)dx = 1.
?
Rx
If f is a density function, then its integral F (x) = ? f (u)du is a
continuous cumulative distribution function (cdf), that is
P(X x) = F (x).
If X is a random variable with this density function, then for any
two real numbers, a and b
Z b
P(a X b) =
f (x)dx.
a
Cathy Poliak, Ph.D. cathy@math.uh.edu Office in FlemingSections
11c (Department
5.5, 6.5 & of
6.6Mathematics University of Houston
Lecture )8 - 3339
3 / 78
Using the cdf F (X ) to Compute Probabilities
Let X be a continuous random variable with pdf f (x) and cdf F (x).
Then for any number a,
P(X > a) = 1 ? F (a)
and for any two numbers a and b with a < b,
P(a X b) = F (b) ? F (a)
Cathy Poliak, Ph.D. cathy@math.uh.edu Office in FlemingSections
11c (Department
5.5, 6.5 & of
6.6Mathematics University of Houston
Lecture )8 - 3339
4 / 78
The Normal distributions
Common type of probability distributions for continuous random
variables.
The highest probability is where the values are centered around
the mean. Then the probability declines the further from the mean
a value gets.
These curves are symmetric, single-peaked, and bell-shaped.
The mean ? is located at the center of the curve and is the same
as the median.
The standard deviation controls the spread of the curve.
If is small then the curve is tall and slim.
If is large then the curve is short and fat.
Cathy Poliak, Ph.D. cathy@math.uh.edu Office in FlemingSections
11c (Department
5.5, 6.5 & of
6.6Mathematics University of Houston
Lecture )8 - 3339
5 / 78
................
................
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
- distributions and sampling umass
- ap statistics normal distributions sampling distributions student handout
- normal models and sampling distributionsteacher culver city high school
- the normal distributions and sampling distributions sections 5 5 6 5 6
- normal distribution university of notre dame
- click and learn sampling and normal distribution educator materials
- chapter 5 class notes sampling distributions loyola university chicago
- chapter 7 sampling distributions 1 introduction
- chapter 6 importance sampling university of arizona
- sampling distribution and properties of summary statistics
Related searches
- translate the graph of f x |3x| 5 down 6 units
- translate the graph of f x 3x 5 down 6 units
- sampling and sampling techniques pdf
- sampling distributions practice problems
- sampling distributions formulas
- 95 5 5 sampling definition
- 5 5 inch 5 56 barrel
- 6 5 vs 6 8 ballistics chart
- sampling distributions calculator
- 14 5 6 5 grendel barrel
- sampling distributions examples in business
- z score standard normal distributions calculator