Question #183082

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.


1
Expert's answer
2021-05-03T04:51:34-0400

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

Given λ=6.\lambda=6. Then


P(X4)=1P(X<4)P(X\geq4)=1-P(X<4)

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

P(X=3)=1e6600!e6611!-P(X=3)=1-\dfrac{e^{-6}\cdot6^0}{0!}-\dfrac{e^{-6}\cdot6^1}{1!}

e6622!e6633!0.8488-\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.



Need a fast expert's response?

Submit order

and get a quick answer at the best price

for any assignment or question with DETAILED EXPLANATIONS!

Comments

No comments. Be the first!
LATEST TUTORIALS
APPROVED BY CLIENTS