Standard +0.3 This is a straightforward application of normal approximation to binomial distribution. Students need to identify n=403, p=0.01, check validity conditions (np and nq both >5), calculate mean and variance, apply continuity correction for P(X<3), and use standard normal tables. While it requires multiple steps, each is routine for S2 level with no conceptual surprises or novel problem-solving required.
2 An airline has found that, on average, 1 in 100 passengers do not arrive for each flight, and that this occurs randomly. For one particular flight the airline always sells 403 seats. The plane only has room for 400 passengers, so the flight is overbooked if the number of passengers who do not arrive is less than 3 . Use a suitable approximation to find the probability that the flight is overbooked.
2 An airline has found that, on average, 1 in 100 passengers do not arrive for each flight, and that this occurs randomly. For one particular flight the airline always sells 403 seats. The plane only has room for 400 passengers, so the flight is overbooked if the number of passengers who do not arrive is less than 3 . Use a suitable approximation to find the probability that the flight is overbooked.\\
\hfill \mbox{\textit{CAIE S2 2017 Q2 [4]}}