The number of cars passing through the M50 toll follows a Poisson distribution with $\lambda = 90,000$ cars per day. What is the probability that more than 450,000 cars pass through in 5 days?

Answer :

Given :

The population mean $(λ) = 90,000$ ( per day )

Find the probability that more than 450000 cars pass through in 5 days

Solution :

The Probability of More Than Four Hundred Fifty Thousand Cars in Five Days :

→ Here we use the population mean $(λ)=5×90,000=450,000$ ( For 5 Days )

$$\text{P}(x > 450{,}000) = \sum_{x=450{,}001}^{\infty} \frac{e^{-\lambda} \cdot \lambda^x}{x!}$$ $$= \sum_{x=450{,}001}^{\infty} \frac{e^{-450{,}000} \cdot 450{,}000^x}{x!}$$ $$= 0.4996$$