Travelers are facing increased costs for both driving and flying to chosen destinations. With rising costs for both modes of transportation, what really weighs on the decision to drive or to fly? To gain a better understanding of the “fly or drive” decision, a recent study compared the costs for trips between Los Angeles and Denver, 1,016 miles one way. Los Angeles to Denver round-trip costs $218 by car and $159.00 by plane. Cost flexibility is greater with the flying trips because of greater airfare choices. The driving trip costs, except for the on-road lunches, are pretty much set in place. Assume the standard deviation for the cost of flying trips is approximately $54.
a. If a flight to Denver from Los Angeles was chosen at random, determine the proportion of the time that the cost would be smaller than $164. Assume the flight costs are bell-shaped.
b. Determine a flight cost that would qualify as the 25th percentile.
c. If nothing can be assumed about the distribution of the flight costs, determine the largest percentile that could be attributed to an airfare of $128.