Rolls-Royce PLC provides forecasts for the business jet market and covers the regional and major aircraft markets. In a recent release, Rolls-Royce indicated that in both North America and Europe the number of delayed departures has declined since a peak in 1999/2000. This is partly due to a reduction in the number of flights at major airports and the younger aircraft fleets, but also results from improvements in air traffic management capacity, especially in Europe.

Comparing January–April 2003 with the same period in 2001 (for similar traffic levels), the average en route delay per flight was reduced by 65%, from 2.2 minutes to 0.7 minutes. The file entitled Delays contains a possible sample of the en route delay times in minutes for 200 flights.

a. Produce a relative frequency histogram for this data.

Does it seem plausible the data come from a population that has an exponential distribution?

b. Calculate the mean and standard deviation of the en route delays.

c. Determine the probability that this exponential random variable will be smaller than its mean.

d. Determine the median time in minutes for the en route delays assuming they have an exponential distribution with a mean equal to that obtained in part b.

e. Using only the information obtained in parts c and d, describe the shape of this distribution. Does this agree with the findings in part a?