Question

The number of parking tickets issued in Raleigh on any given
weekday has a Poisson distribution with parameter (lamda)= 50. What is the
approximate probability that
(a) Between 35 and 70 tickets are given out on a particular day?
(b) The total number of tickets given out during a 5-day week is between
225 and 275?

Answer 1

a) using the cumulative distribution function
\[P(35\le X \le70) = e^{-50}\sum_{k=35}^{70}\frac{50^{k}}{k!} \approx 0.986\]
b) lambda for the week is 50*5 =250
\[[P(225\le X \le275) = e^{-250}\sum_{k=225}^{275}\frac{250^{k}}{k!} \approx 0.893\]

Answer 2

Thanks!!!