(Solved): Potholes on a highway can be a serious problem, and are in constant need of repair. With a particu ...

Potholes on a highway can be a serious problem, and are in constant need of repair. With a particular type of terrain and make of concrete, past experience suggests that there are, on average, \( 2.5 \) potholes per mile after a certain amount of usage. It is assumed that the Poisson process applies to the random variable "number of potholes." Complete parts (a) and (b) below. Click here to view page 1 the table of Poisson probability sums. Click here to view page 2 the table of Poisson probability sums. Click here to view page 3 the table of Poisson probability sums. (a) What is the probability that no more than one pothole will appear in a section of 1 mile? The probability is (Round to four decimal places as needed.) (b) What is the probability that no more than 4 potholes will appear in a given section of 3 miles? The probability is (Round to four decimal places as needed.)