Question

the average number of automobiles per minute stopping for a gas at a particular service station along the coastal road is 3. what is a probability that in any given minute more than two automobile will stop for gas?

Answer 1

We have that

$\mu=3$

x = 2

This follows Poisson distribution

The Poisson probability can be calculated by the formula:

$P(x,\mu)=\frac{e^{-\mu}\mu^x}{x!}$

Need to find $P(x>2,3) = 1 - P(x\le2,3)$

where $P(x\le2,3)= P(0,3)+P(1,3)+P(2,3)$

$P(0,3)=\frac{e^{-3}3^0}{0!}=0.05$

$P(1,3)=\frac{e^{-3}3^1}{1!}=0.15$

$P(2,3)=\frac{e^{-3}3^2}{2!}=0.22$

$P(x>2,3) =1-0.05-0.15-0.22=0.58$

Answer: 0.58