Question

The number of cars that pass through a busy intersection has a Poisson distribution with rate λ=200λ=200cars per hour. What is the probability that no cars pass in a one minute time interval?

Answer 1

Answer: 0.03567

Step-by-step explanation:

The probability mass function for Poisson distribution:-

$P(X=x)=\dfrac{e^{-\mu}\mu^x}{x!}$ , where $\\mu$ = mean of the distribution.

Given : The number of cars that pass through a busy intersection has a Poisson distribution with rate λ=200 cars per hour.

Since 1 hour = 60 minutes.

then , The number of cars that pass through a busy intersection in minute = $\mu=\dfrac{200}{60}=\dfrac{10}{3}$

Let x be the number of cars pass in one minute.

Then, the probability that no cars pass in a one minute time interval will be :

$P(X=0)=\dfrac{e^{-\frac{10}{3}}(\dfrac{10}{3})^0}{0!}$

$=\dfrac{e^{-\frac{10}{3}}(1)}{(1)}=0.0356739933473\approx0.03567$

Hence, the probability that no cars pass in a one minute time interval is about 0.03567.