# STAT

 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 POINTSThe 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. INFLECTION POINT IS A POINT ON THE CURVE WHERE THE CURVUTURE OF THE LINE CHANGES The inflection points are either: u-ou+o 3 identical bell shaped curvatures on one line all have the same ____ but different ____. standard deviationmean Properties of a normal distribution. 1. SYMEMETRIC AND BELL-SHAPED2. COMPLETELY DEFINED BY IT'S MEAN, U, AND STANDARD DEVATION, O3. TOTAL AREA UNDER CURVE IS =14. CURVE DOES NOT CROSS OR TOUCH X AXIS SYMBOLS U AND O U - MEANO- 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 areaThe curve will appear flatterBecause the standard deviation determines the height of the bell shaped distribution PROBABILITY CERTAINLY EQUALS WHY IS X