Traffic flow is traditionally modeled as a Poisson distribution. 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 that no cars pass through the intersection within 30 seconds?

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

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

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