A worker at Disneyworld in Orlando is assigned the task of getting 100 guests to complete a survey about their experience at the park. Suppose each individual guest that the worker asks will agree to complete the survey with a probability of 0.8 and all guests are independent from each other. Let S be the number of guests that the worker needs to ask to fill his quota of surveys.
a) What is the distribution and parameters of S? What is the support?
b) What is the probability that worker fills his quota on the 125th person that he asks to complete the survey?
c) What is the probability that he must ask at least 103 people to fill his quota?
d) What is the average number of people he must ask to fill his quota?
e) Given that it takes him at least 103 people to fill his quota, what is the probability that it takes him between 112 and 115 (inclusive)?