geometric, poisson probability,
7:067 Q SGE all 7:07 Q SGE all 2. [-/3 Points] DETAILS BBUNDERSTAT12 5.4.014.M 4. [-/2 Points] DETAILS BBUNDERSTAT12 5.4.016. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER urnt Mesa Pueblo, in one of the archaeological excavation sites, the artifacts es, the artifact density (number of prehistoric artifacts per 10 liters of The Denver Post reported that, on average, a large shopping center had an incident of shoplifting caught by security 0.9 times every four sediment) was 1.3. Suppose you are going to dig up and examine 50 liters of sediment at this site. Let r = 0, 1, 2, 3, .. be a random hours. The shopping center is open from 10 A.M. to 9 P.M. (11 hours). Let r be the number of shoplifting incidents caught by security in variable that represents the number of prehistoric artifacts found in your 50 liters of sediment. an 11-hour period during which the center is open. (a) Explain why the P probability distribution of r. (a) Explain why the Poisson probability we probability distribution would be a good choice for the random variable r. Find events are independent. O Frequency of shoplifting is a common occurrence. It is reasons is reasonable to assume the events are dependent. Finding prehistoric artifacts is Frequency of shoplifting is me the events are dependent. ants are independent. Finding prehistoric artifacts is a rar the events are dependent Frequency of sho O Finding prehistoric e events are independent Frequent he are dependent. What is A? What is A? (Round your anew mal places.) Write out the formula for the probability distribution of the random variable r. (Use e, ), and r in your answer.) bj What is the probability that from 10 A.M. to 9 P.M. there will be at least one shoplifting incident caught by security? (Round Pin) = your answer to four decimal places.) (bj Compute the probabilities that in your 50 Iners of sediment you will find two prehistoric artifacts, three prehistoric artifacts, and four (c) What is the probability that from 10 A.M. to 9 P.M. there will be at least three shoplifting incidents caught by security? prehistoric artifacts. [Round your answers to four decimal places.) (Round your answer to four decimal places.) P(2) = = (EX (d) what is the probability that from 10 A.M. to 9 P.M. there will be no shoplifting incidents caught by security? (Round your P4 - answer to four decimal places.) (c) Find the probability that you will find three or mar places ] iment. (Round your answer to four decimal Need Help? Read It Watch It () Find the probability that you will find fewer than three prehistoric artifacts in the 50 liters of sediment. (Round your answer to four decimal places.] 5. [-/1.5 Points] DETAILS BBUNDERSTAT12 5.4.013.MI. Need Help? Read It Master It MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER A fishing lake camp boasts that about 90% of the guests catch lake trout over 20 pounds on a 4-day fishing trip. Let n be a random variable that represents the first trip to the camp on which a guest catches a lake trout over 20 pounds. (a) Write out a formula for the probability distribution of the random variable n. 3. [-/2 Points] DETAILS BBUNDERSTAT12 5.4.011.MI. Pin) = MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER (b) Find the probability that a guest catches a lake trout weighing at least 20 pounds for the first time on trip number 3. (Round your answer to three decimal places.) Ise the geometric probability distribution to solve the following problem. in the leeward side of the island of Oahu, in a small village, about 74%% of the residents are of Hawaiian ancestry. Let n - 1, 2,3, - (e) Find the probability that it takes more than three trips for a guest to catch a lake trout weighing at least 20 pounds. (Round resent the number of people you must meet until you encounter the first person of Hawaiian ancestry in the village. your answer to three decimal places.) (2) Write out a formula for the probability distribution of the random variable n. (d) What is the expected number of fishing trips that must be taken to catch the first lake trout over 20 pounds? Hint. Use re for the geometric distribution and round. (Round your answer to two decimal places.) (b) Compute the probabilities that n = 1, n = 2, and n = 3. (found your answers to three decimal places.) Need Help? Read It Master It P12) = P(3) = (c) Compute the probability that n 2 4. Hint: Pin = 4) = 1 - P(n = 1) - P[n = 2) - Pin = 3). (Round your answer e decimal places.) 6. [-/3.25 Points] DETAILS BBUNDERSTAT12 5.4.017. MY NOTES ASK YOUR TEACHER (d) In a more urban part of Oshu, it is estimated that about B an ancestry. Repeat parts (a], (b], and (c) for this part PRACTICE ANOTHER of the island. A television program reported that the U.S. (annual) birth rate is about 24 per 1000 people, and the death rate is about $ per 1000 () Write out a formula for the probability distribution of the random variable n. people. (a) Explain why the Poisson probability distribution would be a good choice he random variable r = number of births (or Pini = deaths) for a community of a given population size? O Frequency of births for deaths] is a common occurrence. It is e the events are dependent (0) Compute the probabilities that n - 1.0 - 2. and n - 3. (Round your answers to three decimal places.) Frequency of births for deat the events are independent. P(1) = Frequency of births (or de events are dependent. Frequency of births for deat e events are independent. P13) = (b) In a community of 1000 people, what is the (annual) probability of 10 births? What is the probability of 10 deaths? What is (in) Compute the probability that n 2 4. Hint: P(n 2 4) = 1 - Pin = 1) - P(n = 2) - Pin = 3) (found your answer to three decimal places ) the probability of 13 births? 13 deaths? (Round your answers to four decimal places.) P(ID births) - P(10 deaths) P(13 births) =[ Need Help? Read It Master It P(13 deaths) - O O
