Sports and Leisure
People who ride in hot-air balloons usually fly just above the treetops at 200-500 feet. In populated areas, however, they usually stay at an altitude of at least 1000 feet. The amount of flying time possible in a hot-air balloon depends on many factors, including the number of propane burners, the number of people in the basket, and the weather. Assume the time spent aloft is normally distributed with mean 1.5 hours and standard deviation 0.45 hour. Suppose a hot-air balloon flight is selected at random.
a. What is the probability that the flight time is between 1 and 2 hours?
b. What is the probability that the flight time is more than 1 hour and 15 minutes?
c. Find a value t such that 10% of all flights last less than t hours.
d. Suppose a person offering hot-air balloon rides charges $50 for each ride of at least 1 hour, and $1.00 for every minute after 1 hour. What proportion of rides costs more than $100?