Question 84753
Hello,

Let's calculate the probability that one student has a score between 500 and 600. This is P(500< X < 620)
I use the notation X for the score:

P(500 < X < 620) 
= P( 500 - 500 < X - 500 < 620 - 500)  (subtract 500 on all sides)

= P(0 < X - 500 < 120)

= P (0/60 < (X-500)/60 < 120/60)       (divide bij 60 on all sides)

= P(0 < (X-500)/60 < 2)

Since X is normally distributed with mean 500 and std 60, we have that 
(X-500)/60 is standardnormally distibuted:

X~N(500,60²) <=> (X-500)/60 ~ N(0,1)

This means that:

= P(0 < (X-500)/60 < 2)  = Phi(2) - Phi(0)

The values of Phi(2) and Phi(0) can be looked up, they are:
Phi(2)= 0.9772 and Phi(0)= 0.5

=> P(0 < (X-500)/60 < 2)  = 0.9972 - 0.5 
                          = 0.4772 
                          ~ 0.48

This means that there is 48% that the score will be wetween 500 and 620.
For 900 students we thus expect that we expect 0.48*900=432 students with a score between 500-620.

Answer: 432