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Standard Scores and Normal Distributions
You should be able to . . .
• Describe the normal density curve
• Describe the standard normal curve
–And know its mean and standard deviation
• Define and compute
z
scores
• Define probability
–Compute simple probabilities
• Define random samples
–Representativeness
Standard Normal Curve
• We will first review the normal curve
–Normal density curve
• We will then discuss a special case of the normal curve
–Standard normal curve
• We will then discuss the scores that make up the standard
normal curve
–Standard scores or
z
scores
Normal curve
• Symmetrical
• Bellshaped
• Unimodal
• Mean = Median = Mode
• When we plot a
smooth
curve instead of a histogram, we are
plotting a
probability density curve
When the probability density function is in the shape of a
normal
curve, it is called a
normal density curve
To Review
Normal curve — this shape:
PLUS
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View Full Document It shows probability
=
Normal Density Curve
Normal Density Curve
• Describes many naturally occurring phenomena
Normal Density Curve
• There are
many possible
normal density curves, each having a
different
mean
and
standard deviation
Normal Density Curve:
Means
• Normal curves will have different means if they are centered
around different values
–e.g., mean IQ vs. mean weight
Normal Density Curve:
Standard Deviations
• Normal curves will have different standard deviations if values
in the distribution cluster around the mean differently
• As standard deviation increases, the distribution flattens
–Low standard deviation
“skinnier” distribution
–High standard deviation
“flatter” distribution
Concept Check
Which distribution has a higher mean?
Which distribution has a higher standard deviation?
Normal Curves
• There are many possible normal curves
–Each with a different mean and standard deviation
• Let’s talk now about one special normal curve
Standard Normal Curve
• Special example of the normal curve
• Always has:
Standard Normal Curve
• The scores that make up the standard normal curve are called
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This note was uploaded on 08/22/2011 for the course PSY 207 taught by Professor Pfordesher during the Fall '07 term at SUNY Buffalo.
 Fall '07
 Pfordesher

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