# Finding Standard deviation and mean value after finding z curve areas

• Jul 3rd 2010, 08:40 PM
cruxkitty
Finding Standard deviation and mean value after finding z curve areas
The diameter length of contact windows used in integrated circuits is normally distributed. About 5% of all lengths exceed 3.75 micrometers and about 1% of all lengths exceed 3.85 micrometers. What is the mean value and standard deviation of the length distribution?

I did a reverse lookup of the z values and got 2 area values for x but what do I do next? I know I should be able to plug this into an equation but I am a little confused how I am suppose to do this.... any help or explanation would be greatly appreciated.
• Jul 3rd 2010, 10:40 PM
Jhevon
Quote:

Originally Posted by cruxkitty
The diameter length of contact windows used in integrated circuits is normally distributed. About 5% of all lengths exceed 3.75 micrometers and about 1% of all lengths exceed 3.85 micrometers. What is the mean value and standard deviation of the length distribution?

I did a reverse lookup of the z values and got 2 area values for x but what do I do next? I know I should be able to plug this into an equation but I am a little confused how I am suppose to do this.... any help or explanation would be greatly appreciated.

remember, $\displaystyle z = \frac {X - \mu}{\sigma}$

Plug in your z values and the corresponding X values. You will then have two equations with two unknowns, $\displaystyle \mu \text{ and } \sigma$. Solve the system simultaneously to find their values.