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)