Many clubs and companies around the country offer hot-air balloon rides. Most impose strict safety regulations and take at most four adults at one time, plus a pilot. The mean weight for an adult male in the United States is 195.5 pounds.28 Suppose the distribution is normal with a standard deviation of 30 pounds.
a. If a hot-air balloon pilot (an adult male) takes three adult males for a ride, what is the distribution for the total weight aboard, T? Carefully sketch the probability distribution for T.
b. If the total weight is less than 900 pounds, the pilot will have enough fuel to extend the ride by a few minutes. What is the probability of an extended ride?
c. If the total weight is over 975 pounds, then the balloon will not be able to take off. What is the probability that the balloon will not be able to take off?
A typical houseplant produces oxygen (from carbon dioxide) in varying amounts, depending on the amount of light and water. Suppose a medium Norfolk Island pine produces 7.5 ml per hour of oxygen when exposed to normal sunlight. Thirty-five Norfolk Island pines are selected at random, and the oxygen output is carefully measured for each. Assume s 5 1.75 ml/h.
a. What is the probability that the sample mean oxygen produced is less than 7 ml/h?
b. What is the probability that the sample mean oxygen produced is between 7.25 and 7.5 ml/h?
c. Suppose each plant is exposed to a new high-intensity grow light and the sample mean oxygen produced for the 35 plants is 8.1 ml/h. Is there any evidence that the new lamp has increased oxygen output?
d. Answer parts (a), (b), and (c) if s 5 3.75 ml/h.