Download AP Statistics: Section 2.2 A

AP Statistics: Section 2.2 A
One particularly important class of
density curves are Normal curves
which describe Normal
distributions. Normal curves are
_________,
single-peaked and
symmetric _____________,
__________.
bell-shaped All Normal
distributions have this same overall
shape.
The density curve for a Normal
distribution is described by giving
its mean ____
 (pronounced myew) and standard deviation ____

(lower case sigma). The mean is
located at the ________________
center of the curve
and is equal to the _______.
median
Changing µ moves the Normal
curve __________
left or right without
changing its spread. The standard
deviation, σ, controls the spread of
the Normal curve.
B
C
D
A
We can locate  by eye on the
curve. As we move out in either
direction from the center , the
curve changes from concave down
(like a ______
frown ) to concave up (like
a ____
cup ). In advanced math
courses, this point is called the
_________________.
point of inflection


Normal distributions are important
in statistics because:
1. Normal distributions are good
descriptions for some distributions of
________.
real data
Examples: scores on test taken by
many people, like the __________;
SAT or ACT
repeated careful measurements of the
same quantity and characteristics of
biological populations, such as
____________
_________________
_.
yields of corn and lengths
of pregnancies
2. Normal distributions are good
approximations to the results of
some ________________.
chance outcomes
Examples: the sum of the dots
showing on 2 dice; the number of
correct answers when guessing on
a T/F or multiple choice test
3. Many statistical inferences based on
Normal distributions work well for
other roughly symmetric
distributions.
Caution: Many sets of data DO NOT
follow a Normal distribution.
Example: personal income is strongly
right-skewed
The 68-95-99.7 Rule (or Empirical Rule)
In the Normal distribution with mean and
standard deviation :
approximately ________
68% of the observations fall
within _______
1 of the mean .
approximately ________
95% of the observations fall
within _______
2 of the mean .
approximately ________
99.7% of the observations fall
within _______
3 of the mean .
95% of the women’s heights lie between
59.5 inches and _______________
69.5 inches
_______________
64.5  2(2.5)
64.5  2(2.5)
What percent of women aged 18 – 24, are
between 62 and 67 inches tall?
______________
68%
A woman aged 18 – 24, who is 72 inches tall is at
what percentile? _______
A woman aged 18 – 24, who is 72 inches tall is at
what percentile? _______
A woman aged 18 – 24, who is 72 inches tall is at
what percentile? _______
A woman aged 18 – 24, who is 72 inches tall is at
what percentile? _______
P99.85
The notation for the Normal
distribution is N (  , ) . For example
N (64.5,2.5)
3, the notation is __________.