Information Technology Reference
In-Depth Information
Fig. 1.1
The figure
illustrates the normal
probability distribution in the
case of
The normal probability density function f
0.02
0.018
N
D
D
x
300 and s
20
0.016
0.014
0.012
0.01
0.008
0.006
0.004
0.002
0
200
220
240
260
280
300
320
340
360
380
400
Number of bagels
long period. From these observations, we can compute
1
the sample mean x and the
sample standard deviation s. Using these two parameters, the normal probability
function is given by
p
2s
e
.xx/
2
1
f.x/
D
:
2s
2
Let us assume that x
D
300 and s
D
20.Thenwehave
p
220
e
.x300/
2
1
f.x/
D
;
(1.1)
220
2
which is plotted in Fig.
1.1
.
Figure
1.1
shows that in most cases, the demand of bagels is around 300. It is
very unlikely that it is above 370 or below 230. More precisely, if we consider any
one particular day, the probability that the demand of bagels is less than b is given by
p
D
Z
b
1
f.x/dx;
(1.2)
1
Suppose we have n measurements resulting in the numbers x
1
;x
2
:::;x
n
. Then the sample mean
is given by
n
X
1
n
x
D
x
j
j
D
1
and the sample standard deviation is given by
s
P
j
D
1
.x
j
x/
2
D
:
s
n
1
For a discussion of these concepts, see any introductory topic in Statistics, e.g., Johnson and
Bhattacharyya [18].
