Question

At a certain location on Highway E31, the number of trucks exceeding the speed limit by more than 10 miles per hour in half an hour is a random variable of interest. The average of this random variable is known as 8.4. What is the probability of a waiting time of less than 5 minutes between cars exceeding the speed limit by more than 10 miles per hour?

Answer 1

Let the random variable $Y$ represent the number of trucks exceeding the speed limit by more than 10 miles per hour in half an hour . $Y$ follows a Poisson distribution with parameter . We need to find the probability that the waiting time is less than 5 minutes between cars exceeding speed limit.

So,

$p(Y\lt5)=\displaystyle\sum^4_{y=0}{e^{-8.4}8.4^y\over y!}={e^{-8.4 }8.4^0\over 0!}+{e^{-8.4 }8.4^1\over 1!}+{e^{-8.4 }8.4^2\over 2!}+{e^{-8.4 }8.4^3\over 3!}+{e^{-8.4}8.4^4\over4!}= 0.07890828$

Therefore, the probability of waiting less than 5 minutes between cars exceeding speed limit is 0.07890828 ,