# Poisson distribution question

An airline has found that the number of people booked on flights who do not arrive at the airport follows a Poisson distribution at the rate of 2% per flight.For a flight with 146 seats ,150 are sold .Use a suitable approximation to find the probability that there are sufficient seats for everyone who arrives . My working - X~Po(2.92) Find Probability ,X≥4 Or 1-P(X= 0,1,2,3) Equals 0.3348 using Poisson distribution . Actual answer is 0.353 Where did I mess up :)

If $$X \sim \mathsf{Pois}(3),$$ then $$P(X \ge 4) = 1 - P(X \le 3) = 0.3527681 \approx 0.353,$$ using R. I'll leave the 'suitable approximation' part to you.
1-ppois(3,3)