Question

(3) Cars driving north on Moraga Road encounter an intersection where they can either continue straight to stay on Moraga Road, or turn right on Saint Mary's Road to head toward SMC. Assume the number of cars that arrive at this intersection between 7:30 and 8:00 am has a Poisson distribution with = 500. A traffic study shows that cars arriving at this intersection at this time of day turn right to head towards SMC with probability 1/3. If Y is a random variable that counts the number of cars that turn towards SMC between 7:30 and 8:00 am, find P(Y > 180).

Answer 1

We will use normal approximation of the Poisson distribution to find the probability below:

Given For - n = 500 Cars that turn (since pa 113) towarsds SMC A Now for a Poisson distribution Mean Variance = Poisson Parametad So here it is 500/ so, SD = √500/ We want PCY > 180) & Using Standard Normal Appronimation - Plz 180 - 500% ] 1500/3 / = P(z ) 1:03) ĈI- P(Z <1.03) -1-0. 8485 20.1515 Ane Soo