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34 Cards in this Set
- Front
- Back
NORMAL PROBABILITY DISTIBUTION
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1. MOST IMPORTANT DISTRIBUTION
2. USED WITH CONTNUOUS RANDOM VARIABLES (THAT ARE EITHER NORMAL OR APPROIMATELY NORMAL DISTURBASTION) |
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A random variable is said to have a normal distribution WHEN
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i it has a probability distribution that is symmetric and bell-shaped see figure 4.1.
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WHAT TWO PARAMETERS THAT ARE N IN THE SHAPE AND POSITION OF A NORMAL DISTRIBUTION CURVE
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THE MEAN
AND STANDARD DEVIATION |
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WHAT IS THE AREA UNDER THE CURVE
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EQUAL TO 1 OR 100%
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THE MEAN
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IS ALSWAYS SMYMMETRIC
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THE SHAPE OF A NORMAL STANDARD DEVIATION IS WHAST
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BELL SHAPED
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THE NORMAL CURVE IS
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BELL SHAPED AND ALWAYS SYMMETRIC
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MEAN IS LOCATED
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IN THE MIDDLE
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MEAN IS THE SAME AS
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MEDIAN
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HOW DO YOU MEASURE THE DISTANCE UNDER THE CURVE
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IN Z SCORES
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TO THE RIGHT OF THE MEAN IS
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POSITIVE
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TO THE LEFT OF THE MEAN IS
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NEGATIVE
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REMEMBER IF AREA IS USED IT MEANS
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PROBAILITY
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When a graph of all such (X, y) points is drawn,
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the normal (bell-shaped) curve will appear.
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a random VARIABLE IS
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A CONTINUOUS DISTRIBUTION WHICH IS USED IN NORMAL DISTRIBUTION
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AREA UNDER THE CURVE IS EQUAL TO
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ONE AND IT IS SYMMETRIC
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When given any normal distribution, we can transform it
into the standard normal distribution by |
standardizing all
the data values. • In other words, convert all x-values into z-scores (or standard scores). |
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ANOTHER NAME FOR Z- SCORE
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STANDARD SCORE
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NAME THREE CONCEPTS THAT MEAN THE SAME
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PERCENT
PROPORTION OR FRACTIONS PROBABILITY OR AREA |
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The z-score is the
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number of standard
deviations that a particular x-value is away from the mean |
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The formula for converting an x-value into a
z-score is: |
Z = VALUE - MEAN
__________________ STANDARD DEVIATION |
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PROPERTIES OF THE STANDARD NORMAL DISTRIBUTION
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1. The total area under the normal curve is equal to 1.
2. The distribution is mounded and symmetrical; it extends indefinitely in both directions, approaching but never touching the horizontal axis. 3. The distribution has a mean of 0 and a standard deviation of 1. 4. The mean divides the area in half (0.50 on each side). 5. Nearly all the area is between z = -3.00 and z = 3.00. (Remember Empirical Rule) (pg 316 |
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Given z-Scores
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We will learn how to find the area under the
standard normal distribution curve for any zscore. Note: Area under curve = Probability • Use Table E “The Standard Normal Distribution Tables”, which you can print from BlackBoard |
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WHAT DOES AREA UNDER THE CURVE MEAN
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PROBABILITY
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THE STANDARD NORMAL DISRIBUTION OF THE STANDARD VARIABLE Z EQUALA
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THE STANDARD SCORE OR THE Z SCORE
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Standard Normal Distribution Tables
•Notice for Table E: |
1.The area given under the curve is the shaded region to the left of the z-score.
2. The curve is symmetric, so the area below –z also equals the area above +z. 3.Total area under the curve equals 1 (which is also total probability). 4.Total area above the mean is 0.5 and total area below the mean is 0.5. |
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Find Areas Given z-Scores (cont’d)
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Step 1: Draw a picture.
Step 2: Shade the area desired. Step 3: Find the corresponding area by using the Standard Normal Distribution Table E. (you may have to manipulate the result) |
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total area under the curve
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is 1
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These Z-scores can then be used to find
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the area (and thus the probability) under the normal curve.
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A Z-score
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is the number of standard deviations that a given x value is above or below the mean. If z represents the Z-score for a given x value then
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Find z-Scores When Given Area (Probability) WHAT MUST YOU DO`
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•Remember to use the table in reverse!!!
•On the inside (or body) of Table E are the areas and on the outside are the z-scores. |
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Find the z-score for the standard normal distribution
WHEN GIVEN AREA IS TO THE RIGHT TAIL . |
1.NEED TO SUBTRACT FROM ONE AND TAKE THE ANSWER TO LOOK UP Z- SCORE
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DESCRIBE THE DISTRIBUTION OF THE STANDARD NORMAL SCORE OF Z?
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A BELL SHAPED CURVE DISTRIBUTION WITH A MEAN 0 AND A STANDARD DEVIATION OF 1
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WHY IS THIS DISTRIBUTION CALLED A STANDARD NORMAL
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THE VARIABLE IS Z; THE STANDARD SCHORE AND THIS DISTRIBUTION IS THE STANDARD OR REFERENCE USED TO DETERMINE THE PROBABIOITIES FOR OTHER NORMAL DITRIBUTIONS
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