In 2012–2013, Carnival Cruise Lines experienced onboard problems with four ships: Triumph, Elation, Dream, and Legend. The technical issues included loss of power, steering problems, and even a fire in an engine room. Despite these setbacks, the cruise industry contributes almost $38 billion to the U.S. economy, and approximately 20% of all people in the United States have taken a cruise.46 Suppose 25 people from the United States are selected at random.
a. Find the probability that exactly three people have been on a cruise.
b. Find the probability that at most two people have been on a cruise.
c. Suppose seven people have taken a cruise. Is there any evidence to suggest that the percentage of people who have taken a cruise has increased? Justify your answer.
The army emphasizes cleanliness and neatness in a military barracks. Each cadet is responsible for maintaining his or her area in top condition. Periodic inspections are held, and those receiving top scores are rewarded. Suppose the mean number of violations discovered per cadet during a barracks inspection is 2.7.
a. What is the probability that a randomly selected cadet will have exactly three violations during an inspection?
b. If a cadet has six or more violations, he or she is assigned to KP duty for one week. What is the probability that a randomly selected cadet will be assigned to KP duty following a barracks inspection?
c. If every member of a 10-cadet unit has no violations, then each will receive a weekend pass. What is the probability of this happening following a barracks inspection?