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Normal Distribution
-6
Normal Distribution
• Probability distribution. It has the following important characteristics: (1)
the curve has a single peak; (2) it is bell-shaped; (3) the mean (average)
lies at the center of the distribution, and the distribution is symmetrical
around the mean; (4) the two tails of the distribution extend indefinitely
and never touch the horizontal axis; (5) the shape of the distribution is
determined by its Mean ( X ) and Standard Deviation (s).
•
X
• As with any continuous probability function, the area
under the curve must equal 1, and the area between two
values of X (say, a and b) represents the probability that X
lies between a and b as illustrated on Figure 1. Further,
since the normal is a symmetric distribution, it has the
nice property that a known percentage of all possible
values of X lie within ± a certain number of standard
deviations of the mean.
.5
X
.5
Adjust graph for information given
• Label the mean given.
• Adjust the standard
deviation according to
instructions
• Use the chart on the
worksheet to calculate
the probability. The
bottom # of the curve
that corresponds to the
# on the chart.
Mean of
problem
Deviation
Deviation
X
Deviation
Deviation
Remember: if asked %,
move decimal 2 places right
and tack on the % sign
Use the same value from
the chart whether + or -
Example
• The shelf life of a particular snack
chip is normally distributed with a
mean of 180 days and a standard
deviation of 30 days
A) About what % of products last
between 150 and 210 days?
B) About what % of products last
between 180 and 210 days?
C) About what % of the products last
more than 210 days?
A).3413  .3413  .6826  68%
B)0  .3413  .3413  34%
C ).5  .3413  .1587  16%
180
150
X
210
240
120
90
270