Test #2a * 2004-11-04
Instructions
Aids permitted: any calculators, any mathematical or
statistical tables, and one sheet of notes (8.5" x 11", one side
only).
Questions
1. Give two interesting facts about the person who discovered Bayes’ Theorem. What was his full name?
2. Because not all airline passengers show up for their seats, an airline sells 125 tickets for a flight that holds only 120 passengers. The probability that a passenger does not show up is 0.1. What is the probability that the flight departs with empty seats? State any assumptions you make.
3. A random sample of size 16 is selected from a population with a mean of 75 and a standard deviation of 8. A second random sample of size 9 is taken from another population with mean 70 and standard deviation 12. Let 
and 
be the two sample means. Find the probability that 
. State any assumptions you make.
4. The time between arrivals of small aircraft at a county airport is exponentially distributed with a mean of 1 hour. What is the probability that more than 3 aircraft arrive within an hour? If 30 separate 1-hour intervals are chosen, what is the probability that no interval contains more than 3 arrivals? State any assumptions you make.
5. Define the following terms: parameter, statistic, sampling distribution.