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```					Normal Distribution

Practice with z-scores
Probabilities are depicted by areas under the curve

•   Total area under the curve is 1
•   Only have a probability from width
– For an infinite number of z scores
each point has a probability of 0
(for the single point)
•   The area in red is equal to p(z > 1)
•   The area in blue is equal to p(-1<
z <0)
•   Since the properties of the normal
distribution are known, areas can
be looked up on tables or
calculated on computer.
Strategies for finding probabilities for
the standard normal random variable.
• Draw a picture of standard normal
distribution depicting the area of interest
• Look up the areas using the table
• Do the necessary addition and subtraction
Find p(0<Z<1.23)
appendix just note the
‘Mean to Z’ column

• .391
Find p(-1.57<Z<0)
• Same thing here, but
doesn’t distinguish
between positive and
negative
• As it is a symmetric
curve, the probability
is the same either
way
• .442
Calculate p(-1.2<Z<.78)
• Here we just find the
‘Mean to z’ for .78,
and then for 1.2, and
together

• .667
Find p(Z>.78)
• This is more the style
of probability we’ll be
concerned with
primarily

• What’s the likelihood
of getting this score,
or more extreme?
• .218
Example: IQ
• A common example is IQ
• IQ scores are theoretically normally
distributed.
• Mean of 100
• Standard deviation of 15
Example IQ
• What’s the probability of getting a score
between 100 and 115 IQ?

P(100  X  115) 
P(100  100  X  100  115  100) 
100  100 X  100 115  100
P(                          
15           15   15
P(0  Z  1)  .3413
Work time...
• What is the area for scores less than: z = -2.5?
• What is the area between z =1.5 and 2.0?
• What z score cuts off the highest 10% of the distribution?
• What two z scores enclose the middle 50% of the
distribution?
– If 500 scores are normally distributed with mean = 50 and
SD = 10, and an investigator throws out the 20 most
extreme scores (10 high and 10 low), what are the
approximate highest and lowest scores that are retained?

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 views: 31 posted: 8/31/2012 language: Unknown pages: 10
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