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

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((3)/(4) )\\= 3.75`

Note: Poisson distribution is

`P(X=k) = (e^(-k) 5^k)/(l!)`