CEGE 3102-we are going to consider a section of the west-bound passing lane

In this problem we are going to consider a section of the west-bound passing lane of Interstate Highway I94 west of the Twin Cities (just east of the Lake Woebegone exit). You are going to consider the number of cracks that require immediate repair along this section of pavement. We will label such cracks: significant cracks.From numerous previous studies, you know that the number of significant cracks is well- modeled by a Poisson distribution with a mean rate of 25 significant cracks per kilometer.a. What is the average spacing between significant cracks?b. What is the probability that there are no significant cracks in a segment of highway 100 meters long?c. What is the probability that at least one significant crack in a randomly selected segment of highway 250 meters long?d. Plot the probability mass function for the number of significant cracks in a 2 kilometer segment of highway.e. What is the probability that there are exactly 50 significant cracks in 2 consecutive kilometers of highway? Note: 50 significant cracks equals 25 significant cracks per kilometer times 2 kilometers, is the expected number of significant cracks for this length of highway.f. How many crack repairs should you budget for if you are repairing 10 kilometers of road? Justify your recommendation using sound statistical reasoning.?g. Consider the three necessary and sufficient conditions for the Poisson distribution. Explain why these assumptions are reasonable (or not) for significant cracks in the in- terstate pavement. Pavement maintenance records show that the number of significant cracks is related to the vehicle load on the highway. How might this enter into your analysis?