Assume the random variable X is normally distrubted with mean = 50 and standard deviation = 7. Compute its probability.
P(34 < X < 61)?
Compute the z-scores for the endpoints of the interval for $\displaystyle X$, then:
$\displaystyle
P(34< X< 61)=P(-16/7<Z<11/7)=P(Z<11/7)-P(Z<-16/7)$ $\displaystyle =\Phi(11/7)-\Phi(-16/7)
$
where $\displaystyle \Phi(z)$ denotes the cumulative standard normal distribution, which you look up in a table.
P(34 < X < 61) =
P( X = 61) - P( X = 34)
Using the formula Z = (X - Mean)/Std Deviation
(61 - 50)/ 7 = 1.57
(34 - 50)/7 = -2.28
ɸ(1.57) - ɸ(-2.28)
ɸ(-2.28) = 1-ɸ(2.28)
As CB mentioned ɸ basically means look it up from a standard normal distribution table
Hope this helps