Answer to Question #183082 in Statistics and Probability for Emmanuel Odoño

Question

Consider the case where the predetermined average number of bus arrivals at the Cubao Station is 6 per 15-minute period. Find the pro of at least 4 buses arriving in a 15-minute period.

Answer 1

Let $X=$ the number of buses bus arrivals at the Cubao Station: $X\sim Po(\lambda).$

Given $\lambda=6.$ Then

$$P(X\geq4)=1-P(X<4)$$

$$=1-P(X=0)-P(X=1)-P(X=2)$$

$$-P(X=3)=1-\dfrac{e^{-6}\cdot6^0}{0!}-\dfrac{e^{-6}\cdot6^1}{1!}$$

$$-\dfrac{e^{-6}\cdot6^2}{2!}-\dfrac{e^{-6}\cdot6^3}{3!}\approx0.8488$$

The probability of at least 4 buses arriving in a 15-minute period is 0.8488.