Download Normal distribution

Normal distribution (3)
When you don’t know
the standard deviation
The Normal Distribution
WRITTEN :
X ~ N ( , )
2
… which means the
continuous random variable X is
normally distributed with mean 
and variance 2 (standard deviation )
Example:
•A machine produces components whose lengths are normally
distributed with a mean of 20cm.
length L ~ N (20, )
2
•Given that 8% of the components produced have a length
greater than 20.5cm ….
P(L>20.5)=8%=0.08
•Find the standard deviation
Example
•A machine produces components whose lengths are normally
distributed with a mean of 20cm.
•Given that 8% of the components produced have a length
greater than 20.5cm, find the standard deviation
length L ~ N (20, )
2
Z
X 
P(L>20.5)=8%=0.08
P( Z 

P(Z<a)=0.92
P(Z>a)=0.08
a
P( Z 
20.5  20

20.5  20

)  0.08
)  1  0.08  0.92
Example contd…
•A machine produces components whose lengths are normally
distributed with a mean of 20cm.
•Given that 8% of the components produced have a length
greater than 20.5cm, find the standard deviation
length L ~ N (20, )
2
P( Z 
P(L>20.5)=8%=0.08
20.5  20

)  0.92
Use inverse normal distribution tables …...
P( Z  a)  0.92
20.5  20

 1.4053
a = 1.4053
0.5

 0.356
1.4053