# Question on normal distribution

• Sep 14th 2010, 09:47 PM
mngeow
Question on normal distribution
The time taken, X seconds, by an automated system to locate an object is
normally distributed with a mean 45 seconds and a standard deviation 30 seconds.
(i) Find the probability P(X > 60).
(ii) Based on the time X, automated systems are classified as “fast”, “normal”
and “slow”. If the middle 80% of all systems are classified as “normal”, find
the cut-off time for a system to be classified as “fast”.
(iii) An automated system is known to have taken longer than 60 seconds to
locate an object, what is the probability that it is among those that have been
classified as “normal”?

I have no idea how to do parts (ii) & (iii)
• Sep 15th 2010, 12:03 AM
Unknown008
Ok, the middle part of your distribution is considered as normal, and this represents 80% of the whole number of systems.

http://p1cture.me/images/96115801816372497718.png

You are asked to find the value of X in my diagram. (Note: I made a mistake and the X should be on the left instead. Sorry about that)

For the last part, find the probability that it takes longer than 60 seconds, that is, find P(X > 60)
Then, find the probability is less than 10% (that is 0.1) then this system is considered as slow. If not, then it's considered as normal.

Post what you come up with! (Happy)
• Sep 15th 2010, 12:31 AM
mngeow
for part(ii),shouldn't the X be on the right?You want to find the cut-off time for "fast" which is in the top 10% isn't it?
• Sep 15th 2010, 12:33 AM
Unknown008
The horizontal axis here represent the time that a system takes.

The shorter time it takes means that it is faster (Wink)
• Sep 15th 2010, 12:39 AM
mngeow
OH.No wonder I got it wrong.Thanks alot man,you're a real life saver!