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WHAT IS THE NORMAL DISTRIBUTION?
IS A CONTINOUS PROBABILITY DISTRIBUTION FOR A GIVEN RANDOM VARIABLE, X, THAT IS COMPLETELY DEFINED BY ITS MEAN AND STANDARD DEVIATION

A NORMAL DISTRIBUTION IS DEFINED BY ITS
MEAN AND STANDARD DEVIATION

NORMAL DISTRIBUTIONS ARE ALL BELL SHAPED. THE MEAN, MODE, AND MEDIUM ARE ____.
ALL THE SAME VALUE.

THE MEAN/MEDIUM/MODE IS LOCATED AT THE CENTER OF A DISTRIBUTION
MEAN

WHAT DETERMINES THE SHAPE OF THE CURVE?
STANDARD DEVIATION

WHAT IS THE STANDARD DEVIATION
 DISTANCE FROM THE MEAN TO ONE OF THE INFLECTION POINTS
 The standard deviation is a statistic that tells you how tightly
 all the various examples are clustered around the mean in a set of data.
 When the examples are pretty tightly bunched together and the
 bellshaped curve is steep, the standard deviation is small. When the
 examples are spread apart and the bell curve is relatively flat, that
 tells you you have a relatively large standard deviation.

INFLECTION POINT
IS A POINT ON THE CURVE WHERE THE CURVUTURE OF THE LINE CHANGES

The inflection points are either:

3 identical bell shaped curvatures on one line all have the same ____ but different ____.

Properties of a normal distribution.
 1. SYMEMETRIC AND BELLSHAPED
 2. COMPLETELY DEFINED BY IT'S MEAN, U, AND STANDARD DEVATION, O
 3. TOTAL AREA UNDER CURVE IS =1
 4. CURVE DOES NOT CROSS OR TOUCH X AXIS

SYMBOLS U AND O
 U  MEAN
 O STANDARD DEVATION

Properties of a Standard Normal Distribution
*special version of the normal distribution
Has the same properties as the normal distribution but always has a MEAN OF 0, and a STANDARD DEVIATION of 1

What kind of curve is this?
Mean 0
Standard deviation 1
Standard Normal Distribution

The larger the standard deviation, the _____ area there will be in the tail of the distribution.
Why
 More area
 The curve will appear flatter
 Because the standard deviation determines the height of the bell shaped distribution

PROBABILITY CERTAINLY EQUALS
WHY IS X<x
 1
 X= THE PROBABILITY, WHICH MUST BE EQUAL OR LESS THAN 1

What does the z score do?
The z score is a formula t/f
transforms a normal random variable into a standrard normal random variable.
True
Z= xu / o

HOW WOULD YOU WORD THE EQUATION OF A PROBABIILTY THAT IS BETWEEN 6591530. WHICH WAYS ARE THE SYMBOLS FACING?
 P (659 < X < 1530)
 < TO THE LEFT

THE CUMMULATIVE STANDARD NORMAL TABLE GIVES US THE ANSWERS FOR PROBABILITYS OF THE LEFT/RIGHT OF Z.
LEFT

TABLE TO LOOK UP PROBABILITIES
CUMMULATIVE STANDARD NORMAL TABLE

THE "Z VALUE" CORRESPONDS TO
THE PROBABILITY GIVEN BY THE CHART.

GIVEN: X=46.2, U=46 AND O=1.4. INDICATE WHERE ON THE CURVE THE X VALUE WOULD BE.
 IT WOULD BE ON THE HORIZONTAL LINE, AFTER 46
 40.4_________46___X________51.6

What does the z score do?
The zscore (z) can transform a normal random variable into a standard normal random variable.

