P Bands will randomly survey people around various parts of campus. The survey taker, Jorge, wants...
P Bands will randomly survey people around various parts of campus. The survey taker, Jorge, wants to find people who attended a P Band performance last semester. From previous surveys, Jorge knows that the probability a person on campus did not attend a P Band performance last semester was 0.68.
a) Let B be the number of people surveyed until the representative finds a person who did attend a P Band performance last semester. What is the distribution, parameter(s) and support of B?
b) What are the average and standard deviation of B?
c) What is the probability Jorge surveys at least 4 people until he finds a person who attended a P Band performance last semester?
d) Find the probability Jorge surveys between 3 people and 5 people (inclusive) until he finds one who attended a P Band performance last semester.
e) Jorge has already surveyed 3 people and has not found any who attended a P Band performance last semester. What is the probability it takes him at most 9 people to find one who attended a P Band performance last semester?
f) Jorge needs to find 15 people who have attended a P Band performance last semester. How many should he expect to survey in order to find 15 people who attended a performance last semester? What distribution, parameter(s), and support are you using?
g) Find the standard deviation of the number of people needed to find 15 who attended a P Band performance last semester.
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