Any help offered in solving the below question will be much appreciated.
In a local hospital , on average 3.5 cases of diarrhea per week and each case is independent of the other similar cases.
Taking a week as consisting as 7 working days.
a) Show that the probability that the doctor sees at most 2 cases of diarrhea in a day is 0.986.
b) Using a suitable approximation, find the probability that, in a random sample of 100 days, there will be more than 96 days in which the doctor sees at most 2 cases of diarrhea in a day. (0.946)