Let S be the number of seats in the aircraft;
T be the number of tickets sold;
p be the probability that any given passenger arrives for the flight.

Let X be the number of passengers that arrrive for a given flight.

Then X has the Binomial distribution for T trials with the probability of success 0.95. You can calculate the mean m and variance s2 for this distribution.

In order to avoid lengthy calculations in the discrete case we approximate the Binomial distribution by a Normal distribution with the same mean and variance, i.e. by
N(m,s2).

Thus we now assume that X has distribution N(m,s2). In order to use the standard Normal probability tables N(0,1) we have to put
Y = X-m
s
 ;
then Y has distribution N(0,1).

So as to allow for the approximation to the discrete data by the continuous Normal distribution, we want to find Prob[X £ 400.5] and look up the probability for the corresponding value of Y in the Normal table.

If you use a Normal distribution table you need to check to see if it gives the area F(Y) under the Normal curve to the left of Y, that is the probability that the variable is less than Y, or to the right of Y.