The problem said:
An airplane has 120 seats. The probability that a ticketed passenger will show up for a flight is 0.95. Assume that all passengers act independently and that the airline has sold 130 tickets for a particular flight. Using the Normal approximation to the Binomial (with appropriate continuity correction), compute the approximate probability that the flight will be overbooked.
I know I need to use the central limit theorem, and I start by defining indicator variables:
Xi= 1 if passanger i show up for a fligth, 0 otherwise.
Then the approximate probability that the flight will overbooked, defined by even OB is:
P(OB)=P(sum from 1 to 130 of Xi > 120)
I know also that P(xi)=0.95
But I'm missing something to finish this problem, and found the correct solution wich the book said is: 0.886 or 88.6%. Thanks for your help.