Any help offered in solving the below question will be much appreciated.
Thanks
Kingman
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)
Part B is confusing. It tells you to use the appropriate approximation to solve but then asks you a to find a different probability.
Can you double check to make sure you posted the question correctly? Maybe there were three parts.
a)solve by poisson
b)solve by approximation of poisson
c)solve the new probability
Maybe I'm missing something that someone else can point out