# diagnostic - Fall 2006 Statistics Diagnostic Mark Hansen...

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Fall Mark Hansen 2006 Transportation Engineering Statistics Diagnostic 1. Vehicles cross a cordon line of a rural highway at a uniform rate between the hours 9am and 10am. The crossing time of an individual vehicle is equally likely to have any value with this time range. The cordon crossing times of 25 randomly chosen vehicles crossing the cordon between these times are recorded and averaged. What is the probability that the average time obtained will be earlier than 9:24? 2. An airline is considering replacing a 30-seat jet with a 12-seat jet for a regular daily flight. With the 30-seat jet, the number of passengers carried is Poisson distributed with a mean of 9. If the 12-seat jet is used instead, what proportion of the time will it be full? What will be the expected number of “spilled passengers”—those lost because no seats are available on the day they want to fly? 3. Calculate the mean and variance, and qualitatively describe the skewness, of a random variable with the following CDF: 0 0.75 1 .7 1 -1

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diagnostic - Fall 2006 Statistics Diagnostic Mark Hansen...

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