Final answer:
Calculating the exact probabilities for Delta having a certain number of mishandled bags per 1,000 passengers requires the use of statistical methods like the Poisson distribution. However, the probabilities of no mishandled bags and at least one mishandled bag can be conceptually related where the latter is the complement of the former. Exact probabilities cannot be provided here without further computation.
Step-by-step explanation:
The student asked about the probability of mishandled bags by Delta airline given a statistic from the U.S. Department of Transportation. Delta had 7.1 mishandled bags per 1,000 passengers in 2005.
a. No mishandled bags
To find the probability of Delta having no mishandled bags among the next 1,000 passengers, we would assume a Poisson distribution which models the number of occurrences of an event in a specific interval. However, since this distribution requires a known rate of occurrence and we are working with historical data, the actual computations would be complex and require statistical software or tables. Thus, this is just a hypothetical exercise, and an exact answer cannot be provided here without further information.
b. At least one mishandled bag
The probability of at least one mishandled bag can be derived from the complement of having no mishandled bags: P(at least one) = 1 - P(none).
c. At least two mishandled bags
Similarly, the probability of having at least two mishandled bags would involve more complex statistical calculations, typically using the cumulative distribution function of the Poisson distribution.