Download Power Point Normal dist Z-scores-HRW- in 09-10

Survey
yes no Was this document useful for you?
   Thank you for your participation!

* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project

page
1
page
2
page
3
page
4
page
5
page
6
page
7
page
8
page
9
page
10
page
11
page
12
page
13
page
14
page
15
page
16
page
17
page
18
Document related concepts
no text concepts found
Transcript 
12.6 Normal Distributions
Objectives
• Use z-scores to find percentiles.
• Thinking Skill: Explicitly assess
information and draw conclusions
Copyright © by Holt, Rinehart and Winston. All
12.6 Normal Distributions
Glossary Terms
normal curve
normal distribution
standard normal curve
z-score
Copyright © by Holt, Rinehart and Winston. All
12.6 Normal Distributions
Rules and Properties
Properties of Normal Distributions
• Symmetric about the mean, x .
• Total area under the curve is 1.
• Mean, median, and mode are
about equal.
Copyright © by Holt, Rinehart and Winston. All
Copyright © by Holt, Rinehart and Winston. All
12.6 Normal Distributions
Rules and Properties
Properties of Normal Distributions
• About 68% of the area is within 1
standard deviation of the mean.
Copyright © by Holt, Rinehart and Winston. All
12.6 Normal Distributions
Rules and Properties
Properties of Normal Distributions
• About 95% of the area is within 2
standard deviations of the mean.
Copyright © by Holt, Rinehart and Winston. All
12.6 Normal Distributions
Rules and Properties
Properties of Normal Distributions
• About 99.8% of the area is within
3 standard deviations of the
mean.
Copyright © by Holt, Rinehart and Winston. All
Translation of data values
into standard scores
• The z-score is a standard score.
• z-score is the number of
______________ ____________
a score is from the __________
• Formula for z-score:
Copyright © by Holt, Rinehart and Winston. All
12.6 Normal Distributions
Rules and Properties
z-Score
x-x
z=

normal distribution
mean: x
any data value: x
standard deviation: 
Copyright © by Holt, Rinehart and Winston. All
• Questions on your
homework?
Copyright © by Holt, Rinehart and Winston. All
Percentiles
• The area under the entire curve
is one or 100% of the scores
• So area up to a score is the
percentile for that score – the
percent of scores lower than that
score
Copyright © by Holt, Rinehart and Winston. All
Try this:
• Standardized test scores are
normally distributed with a mean
of 100 and a standard deviation
of 10.
• What percent scored less than
95?
Copyright © by Holt, Rinehart and Winston. All
Indicate on the drawing what we are
looking for.
Find the z-score
Can’t tell % using the Empirical rule.
Copyright © by Holt, Rinehart and Winston. All
This table gives
the percents for
any given z-score
Copyright © by Holt, Rinehart and Winston. All
• The z-score for a score of
95 is -.5
• The table shows that the
percent of scores lower
than a z-score of -.5 is
30.85%
Copyright © by Holt, Rinehart and Winston. All
Try some more:
• What is the percent below 120?
Copyright © by Holt, Rinehart and Winston. All
• What is the percent higher than
112? (be careful!!)
Copyright © by Holt, Rinehart and Winston. All
• What is the percent scoring
between 90 and 115?
Copyright © by Holt, Rinehart and Winston. All
Related documents