The Boston Fire Department receives 911 calls at a mean rate of 1.6 calls per hour (Mass. gov website, November 2012). Suppose the number of calls per hour follows a Poisson probability distribution.

a. What is the mean time between 911 calls to the Boston Fire Department in minutes?

b. Using the mean in part (a), show the probability density function for the time between 911 calls in minutes.

c. What is the probability that there will be less than one hour between 911 calls?

d. What is the probability that there will be 30 minutes or more between 911 calls?

e. What is the probability that there will be more than 5 minutes but less than 20 minutes between 911 calls?