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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
WHAT DETERMINES THE SHAPE OF THE CURVE?
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
- bell-shaped 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.
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 BELL-SHAPED
- 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?
Standard deviation- 1
Standard Normal Distribution
The larger the standard deviation, the _____ area there will be in the tail of the distribution.
- 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
- 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.
Z= x-u / o
HOW WOULD YOU WORD THE EQUATION OF A PROBABIILTY THAT IS BETWEEN 659-1530. 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.
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
What does the z score do?
The z-score (z) can transform a normal random variable into a standard
normal random variable.