please answer the problem below and show all work for all parts of the question. You can calculate values of any function you need with excel, or online program/calculator if necessary. Thanks!

4. Suppose the given country road has large defects which are distributed along its length according to Poisson distribution with an average of 2 defects per mile. It takes the crew repairing these defects one full day to x one of them. They move along the road and repair the defects as they are found. a) If the road is 10 miles long what is the probability they will be done in three weeks (15 working days)? b) What is the probability they will get at least to the middle of the road (i.e. advance by at least 5 miles) by the end of the second week (after 10 working days)? 0) What is the mean and standard deviation of the length of the road they will cover by the end of the second week