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 aPoisson 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 between911 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 minutesbetween 911 calls?
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
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
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
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?
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