Copyright © 2006 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
Slide 6- 1
Copyright © 2006 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
Chapter 6
The Standard Deviation as aRuler and the Normal Model
Copyright © 2006 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
Slide 6- 3
Finding Normal Percentiles Using Technology
Many calculators and statistics programs have theability to find normal percentiles for us.
Copyright © 2006 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
Slide 6- 4
Finding Normal Percentiles Using Technology
What is the probability of an observation between0 and 1.34 in the normal curve where the mean is0 and the standard deviation is 1?
What is the probability of an observation less thanz=1.34 in the normal curve where the mean is 0and the standard deviation is 1?
Find the probability that an observation fallsbetween 0 and .78 where the mean is .5 and thestandard deviation is 1.
Copyright © 2006 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
Slide 6- 5
Finding Normal Percentiles Using Technology
Find the probability that an observation fallsabove -1.62 where the mean is 2 and thestandard deviation is 3.
Consider a normal distribution where the mean is56.8 and the standard deviation is 5.5. What isthe probability of an observation between 60 and70?
Consider a normal distribution where the mean is10 and the standard deviation is 15. What is theprobability of an observation larger than 20?
Copyright © 2006 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
Slide 6- 6
From Percentiles to Scores: z in Reverse
Sometimes we start with areas and need to findthe corresponding z-score or even the originaldata value.
Example: What z-score represents the firstquartile in a Normal model where the mean is 0and the standard deviation is 1?
Copyright © 2006 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
Slide 6- 7
From Percentiles to Scores: z in Reverse
Consider a normal distribution where the mean is55 and the standard deviation is 15. What is the63rd percentile? What is the 12th percentile?
Scores on a particular test follow a normaldistribution with a mean of 75.6 and a standarddeviation of 7.8. Find the score separating thetop 15% of the scores from the bottom 85% ofscores.