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Chapter 5
Some Key Ingredients for Inferential
Statistics: The Normal Curve,
Probability, and Population Versus
Sample
The Normal Distribution
 Normal curve
The Normal Distribution
 Normal curve and percentage of scores
between the mean and 1 and 2
standard deviations from the mean
The Normal Distribution
 The normal curve table and Z scores
– Gives the precise percentage of scores
between the mean (Z score of 0) and any
other Z score
– Table lists positive Z scores
The Normal Distribution
 Steps for figuring the percentage above
of below a particular raw or Z score:
1. Convert raw score to Z score (if necessary)
2. Draw normal curve, where the Z score falls
on it, shade in the area for which you are
finding the percentage
3. Make rough estimate of shaded area’s
percentage (using 50%-34%-14% rule)
The Normal Distribution
 Steps for figuring the percentage above
of below a particular raw or Z score:
4. Find exact percentage using normal
curve table
5. If needed, add or subtract 50% from
this percentage
6. Check the exact percentage is within
the range of the estimate from Step 3
The Normal Distribution
 Steps for figuring Z scores and raw
scores from percentages:
1. Draw normal curve, shade in
approximate area for the percentage
(using the 50%-34%-14% rule)
2. Make rough estimate of the Z score
where the shaded area starts
3. Find the exact Z score using the
normal curve table
The Normal Distribution
 Steps for figuring Z scores and raw
scores from percentages:
4. Check that your Z score is similar to
the rough estimate from Step 2
5. If you want to find a raw score, change
it from the Z score
Probability
 Probability
– Expected relative frequency of a particular
outcome
 Outcome
– The result of an experiment
Possible successful outcomes
Probabilit y 
All possible outcomes
Probability
 Range of probabilities
– Proportion: from 0 to 1
– Percentages: from 0% to 100%
 Probabilities as symbols
–p
– p < .05
 Probability and the normal distribution
– Normal distribution as a probability
distribution
Sample and Population
 Population
 Sample
 Methods of sampling
– Random selection
– Haphazard selection
Sample and Population
 Population parameters and sample
statistics
Controversies and Limitations
 Is the normal curve really so normal
 What does probability really mean?
 Sample and population