Download Normal Distribution

6.2 Use Normal Distributions
Pg. 219
Vocabulary
• Normal Distribution
– Modeled by a “bell-shaped” curve
• Normal Curve
– The “bell-shaped” curve is symmetric about the mean
• Horizontal Reflection
• Standard Normal Distribution
– The normal distribution with a mean of 0 (zero) and a
standard deviation of 1 (one). The formula below can be used
to transform  -values from a normal distribution with
mean (  ) and standard deviation  into z-values having a
standard normal distribution

z

The Normal Distribution







Empirical Rule: 68-95-99.7
• For a normal distribution, nearly all values lie
within 3 standard deviations of the mean.
• About 68% of the values lie within 1 standard
deviation of the mean, 95% of the values lie
within 2 standard deviations of the mean, and
99.7% of the values lie within 3 standard
deviations of the mean.
z - Score
• The z–value for a
particular  –value
(“mu” value) is called
the z–score for the
 -value and is the
number of standard
deviations the  –
value lies above or
below the mean .
• To find the
probability that z is
less than or equal to
some given value, we
must use the table
(pg 248)
Example #1, Find a normal probability
• A normal distribution has a mean of (  ) and a
standard deviation ( ) . For a randomly
selected  –value from the distribution.
– Find…


P       3
P       3


 0.34  0.135  0.023

0.4985




 

• We want the total probability that a randomly
selected  – value lies between  and   3
Example #2
• Interpret normally distributed data
– The heights of 3000 women at a particular college are
normally distributed with a mean of 65 inches and a standard
deviation of 2.5 inches. About how many of these women
have heights between 62.5 inches and 67.5 inches?
• First find where 62.5 and 67.5 are on the bell curve.
– This area represents 68% on either side of the mean
– So .68(3000)=2040
– 2040 women at this college have
heights between 62.5 and 67.5 inches
Example #3
• Find the probability that a randomly selected woman has a
height of at most 68 inches.
Homework
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