Download normal distribution

14
Descriptive Statistics
What a Data Set Tells Us
Copyright © 2014, 2010, 2007 Pearson Education, Inc.
Section
Section14.4,
1.1, Slide
Slide11
14.4 The Normal Distribution
• Understand the basic properties
of the normal curve.
• Relate the area under a normal
curve to z-scores.
• Make conversions between raw
scores and z-scores.
• Use the normal distribution to
solve applied problems.
Copyright © 2014, 2010, 2007 Pearson Education, Inc.
Section 14.4, Slide 2
The Normal Distribution
The normal distribution describes many real-life
data sets. The histogram shown gives an idea of
the shape of a normal distribution.
Copyright © 2014, 2010, 2007 Pearson Education, Inc.
Section 14.4, Slide 3
The Normal Distribution
Copyright © 2014, 2010, 2007 Pearson Education, Inc.
Section 14.4, Slide 4
The Normal Distribution
We represent the mean by μ and the standard
deviation by σ.
Copyright © 2014, 2010, 2007 Pearson Education, Inc.
Section 14.4, Slide 5
The Normal Distribution
• Example: Suppose that the distribution of
scores of 1,000 students who take a
standardized intelligence test is a normal
distribution. If the distribution’s mean is 450 and
its standard deviation is 25,
a) how many scores do we expect to fall between
425 and 475?
b) how many scores do we expect to fall above
500?
(continued on next slide)
Copyright © 2014, 2010, 2007 Pearson Education, Inc.
Section 14.4, Slide 6
The Normal Distribution
• Solution (a): 425 and 475
are each 1 standard
deviation from the mean.
Approximately 68% of the
scores lie within 1 standard
deviation of the mean.
We expect about
0.68 × 1,000 = 680 scores
are in the range 425 to 475.
(continued on next slide)
Copyright © 2014, 2010, 2007 Pearson Education, Inc.
Section 14.4, Slide 7
The Normal Distribution
Solution (b):
We know 5% of the
scores lie more than
2 standard
deviations above or
below the mean, so
we expect to have
0.05 ÷ 2 = 0.025 of
the scores to be
above 500. Multiplying by 1,000, we can expect
that 0.025 * 1,000 = 25 scores to be above 500.
Copyright © 2014, 2010, 2007 Pearson Education, Inc.
Section 14.4, Slide 8