During the Cold War there were frequent radio tests of alert warnings. The regular program was interrupted and replaced by a long high-pitched signal. An announcer would break in with a message similar to, “This has been a test of the emergency broadcasting system.’’ Suppose the time (in hours) between these tests had an exponential distribution with mean 24 hours.
a. If a test occurred at 6:00 a.m., what is the probability that another one would occur before 6:00 p.m.?
b. If a test occurred at 10:00 p.m., what is the probability that another one would not occur until after 6:00 a.m.?
c. If a test occurred at 9:00 a.m., what is the probability that the next test would occur between 12:00 p.m. and 1:00 p.m.?
The U.S. Public Health Service’s Advisory Committee on Immunization Practices recommends a tetanus booster every 10 years. Suppose the lifetime (in years) of a tetanus booster shot has an exponential distribution with l 5 0.05.
a. Find the probability that a randomly selected tetanus booster shot is still protecting against tetanus after more than 10 years.
b. Suppose a physician recommends a booster shot after a period when only 10% of all tetanus shots still have an effect. How long should you wait before getting another booster shot?
c. Suppose two people independently receive tetanus shots. What is the probability that both shots still have an effect after more than five years?