Assume the fire department guidelines are correct and that they respond to an average of 15 emergency incidents per day. Use the graph of the Poisson distribution and technology to show the actual probability using Poisson probability to answer the following questions. Explain your reasoning and show your work with probabilities and commands used in the calculator or Excel.
1. On a random day, what is more likely, 15 emergency incidents or at least 20 incidents?
2. On a random day, what is more likely, 14 to 16 emergency incidents or less than 14 incidents?
3. On the 4th of July, the fire department responds to 21 incidents. Is there reason to believe the guidelines should be adjusted for this holiday?