Final answer:
After calculating 28.6% of 15,422 people, which represents those not protected by the flu vaccine, approximately 4,411 people are likely to get influenza.
Step-by-step explanation:
A study shows that an influenza (flu) vaccine is 71.4% effective in preventing a particular type of influenza. If 15,422 people receive the vaccine, we can calculate the number of people who would not be protected by finding the percentage who would not be protected (which is 100% - 71.4% = 28.6%) and applying it to the total number of people vaccinated.
To find out how many people are likely to get influenza despite being vaccinated:
Calculate the percentage who are not protected: 100% - 71.4% = 28.6%.
Apply this percentage to the total number of people vaccinated: 28.6% of 15,422 is approximately 4,411 (rounded to the nearest whole number).
Therefore, about 4,411 people would not be protected and would be likely to get influenza.