Unless stated otherwise in the exercise, use software to find the exact Poisson.

Question 5.54

5.54 Mishandled baggage.

In the airline industry, the term “mishandled baggage” refers to baggage that was lost, delayed, damaged, or stolen. In 2013, American Airlines had an average of 3.02 mishandled baggage per 1000 passengers.14 Consider an incoming American Airlines flight carrying 400 passengers. Let be the number of mishandled baggage.

  1. Use the binomial distribution to find the probability that there will be at least one mishandled piece of baggage.
  2. Use the Normal approximation with continuity correction to find the probability of part (a).
  3. Use the Poisson approximation to find the probability of part (a).
  4. Which approximation was closer to the exact value? Explain why this is the case.