Solving Airline Problem: Probability & Reservations

[moltoor]

Ok, I was looking at some solutions and they don't seem correct. Here is the problem:
An airline knows that the probability a person holding a reservation on a certain flight will not appear is 10%. The plane holds 90 people.
a) If 95 reservations have been solf, find the prob. that the airline will be able o accommodate everyone appearing on the plane.
b) How many reservatiosn should be sold so that the ariline can accommodate everyone who appears for the flight 99% of the time?

 

[ssd]

Is it not a homework problem?
Solution: Assume that arrival of a person with reservation is independent of other passengers.
Let X be the no. of passengers with reservation who finally turns up and N be the no. of reservations issued.
a) X~Bin(95,0.9). Find P(X<=90).
b) Find N such that P(X<=90)=0.99, when X~Bin(N,0.9).