1
Handout 8. Chapter 6
The Normal Distribution
.
Continuous random variables can assume the infinitely
many values corresponding to points on a line interval.
(Think of a discrete random variable whose range of values
becomes denser and denser.)
•
Examples:
Heights, weights ,length of life of a particular
product
• The probability distribution becomes approximately a smooth
function. This is called the
probability density function, f(x).
d
a
r
y
p
o
i
n
t
o
f
s
o
m
e
c
l
a
s
s
,
Suppose that the birth weights of 100 babies are recorded
Recall:
The total area under the histogram is 1.
the data grouped in class intervals of 1 pound
Next, we suppose that the number of measurements is increased to 5000
and they are grouped in class intervals of .25 pound.
The
probability density function
f
(
x
) describes the distribution of
probability for a continuous random variable. It has the properties:
•
1.
The total area under the probability density curve is 1.
•
2.
P
[
a
≤
X
≤
b
] = area under the probability density curve between
a
and
b
.
P( a<X<b)= P( a
≤
X
≤
b) = P( a
<
X
≤
b) = P( a
≤
X
<
b) .
•
3.
f
(
x
)
≥
0 for all
x
.
With a continuous random variable, the probability that
X
=
x
is
always
0. It is only meaningful to speak about
the probability that
X
lies in an interval.
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 Spring '08
 palmero
 Normal Distribution, $1, 5%, $0, $0.5, $1.5

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