Question

The number of tickets issued by a meter reader for parking-meterviolations can be modeled by a Poisson process with a rateparameter of five per hour.
a. What is the probabilitythat exactly three tickets are given out during a particularhour?

b. What is the probabilitythat at least three tickets are given out during a particularhour?

c. How many tickets do youexpect to be given during a 45-min period?

Answer 1

Answer:

Step-by-step explanation:

Let X be the  number of tickets issued by a meter reader for parking-meterviolations can be modeled by a Poisson process with a rateparameter of five per hour.

X is Poisson with parameter =5per hour

a) the probabilitythat exactly three tickets are given out during a particular hour

=$P(X=3)=0.14037$

b)  the probabilitythat at least three tickets are given out during a particularhour

=$P(X\geq 3) =0.87534$

c) tickets we expect to be given during a 45-min period

=$5(\frac{3}{4} )\\= 3.75$

Note: Poisson distribution is

$P(X=k) = \frac{e^{-k} 5^k}{l!}$