Traffic flow is traditionally modeled as a Poisson dis- tribution. A traffic engineer monitors the traffic flowing through an intersection with an average of six cars per minute. To set the timing of a traffic signal, the following probabilities are used.

(a) What is the probability of no cars through the intersection within 30 seconds?

(b) What is the probability of three or more cars through the intersection within 30 seconds?

(c) Calculate the minimum number of cars through the inter- section so that the probability of this number or fewer cars 30 seconds is at least 90%. in

(d) If the variance of the number of cars through the intersec- tion per minute is 20, is the Poisson distribution appropriate? Explain.