Download HAS A GAUSSIAN DISTRIBUTION WITH A MEAN

A random voltage x(t ) has a Gaussian (Normal) distribution with a mean value of
  0V and a stand deviation of   10V . A single random sample x(t ) is taken.
Determine the following probabilities:
Solution:
The standard normal distribution is a normal distribution with a mean of 0 and a standard
deviation of 1. A normal distribution with a mean  and a standard deviation  can be
x x
 .
transformed to standard normal distributions by the formula: z 

10
From z-table:
Px  0  Pz  0  0.5
Px  10  Pz  1  0.159
Px  10  Pz  1  0.159
P10  x  10  P1  z  1  0.683
(e) P x  10  Px  10  P( x  10)  Pz  1  P( z  1)  0.317
(a)
(b)
(c)
(d)
(f) Px  20  Pz  2  0.02275
(g) P x  20  Px  20  P( x  20)  Pz  2  P( z  2)  0.0455