Question

The average number of automobiles per minute stopping for gas at a particular service station along the coastal road is 4 what is the probability that in any given minute more than two will stop for gas

Answer 1

We have that

$\mu=4$

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 $P(x>2,4) = 1 - P(x\le2,4)$

where $P(x\le2,4)= P(0,4)+P(1,4)+P(2,4)$

$P(0,4)=\frac{e^{-4}4^0}{0!}=0.0183$

$P(1,4)=\frac{e^{-4}4^1}{1!}=0.0733$

$P(2,4)=\frac{e^{-4}4^2}{2!}=0.147$

$P(x>2,4) =1-0.0183-0.0733-0.147=0.7614$

Answer: 0.7614