Psychology and Human Behavior
As a result of stricter training requirements, fewer big fires, higher-paying jobs in cities, and changes in society, the number of volunteer firefighters is declining. Approximately three-fourths of all firefighters in the United States are volunteers, and the total number of volunteer firefighters has decreased steadily over the last two decades. Suppose 30 U.S. firefighters are selected at random.
a. Find the probability that exactly 22 of the firefighters are volunteers.
b. Find the probability that more than 25 of the firefighters are volunteers.
c. Suppose 17 of the firefighters are volunteers. Is there any evidence to suggest that the proportion of volunteer firefighters has decreased? Justify your answer.
d. Suppose 50 firefighters are selected at random from the West and 50 firefighters are selected from the Northeast. What is the probability that at least 40 of the firefighters will be volunteers in both groups?