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 $(\lambda )=90,000$ ( 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 $(\lambda )=5\times 90,000=450,000$ ( For 5 Days )

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