Question

Suppose p is the number of cars per minute passing through a certain road junction between 5 PM and 6 PM, and p has a Poisson distribution with mean 3. What is the probability of observing fewer than 3 cars during any given minute in this interval?

• A. $8/\left(2e^3\right)$
• B. $9/\left(2e^3\right)$
• C. $17/\left(2e^3\right)$
• D. $26/\left(2e^3\right)$

Answer 1

The correct option is C $17/\left(2e^3\right)$

x = {Number of cars per minute}

Av. Number of cars

$\left(\lambda \right)=3/min.$

So $P(x<3)=P(x\le 2)$

$=P(x=0)+P(x=1)+P(x=2)$

$=e^{-\lambda }[\frac{{\lambda }^0}{0}+\frac{{\lambda }^1}{1}+\frac{{\lambda }^2}{2}]$

$=e^{-3}[1+3+\frac{9}{2}]=\frac{17}{2e^3}$