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- V 5.4 Hmwk 7 Geometric & Poissor' X t t t 6 9 O Q Q https://www.webassignnet/web/Student/AssignmentResp... A\" {3 Oi Eh 5:: g . {3 l {'5 . .1 nzrnrwtrnrcrrcrrcn mmm In western Kansas, the summer density of hailstorms is estimated at about 3.1 storms per 5 square miles. In most cases, a hailstorm damages only a relatively small area in a square mile. A crop insurance company has insured a tract of 10 square miles of Kansas wheat land against hail damage. Let rbe a random variable that represents the number of hailstorms this summer in the 10squaremile tract. (3) Explain why a Poisson probability distribution is appropriate for r. 0 Hail storms in western Kansas are a common occurrence. It is reasonable to assume the events are dependent. (9 Hail storms in western Kansas are a rare occurrence. It is reasonable to assume the events are independent. 0 Hail storms in western Kansas are a rare occurrence. It is reasonable to assume the events are dependent. O Hail storms in western Kansas are a common occurrence. It is reasonable to assume the events are independent. \\f What is A for the 10-square-mile tract of land? Round 11 to the nearest tenth so that you can use Table 4 of Appendix II for Poisson probabilities. : (b) If there already have been two hailstorms this summer, what is the probability that there will be a total of four or more hailstorms in this tract of land? Compute P(r 2 4 | r 2 2). (Round your answer to four decimal places.) : (c) If there already have been three hailstorms this summer, what is the probability that there will be a total of fewer than six hailstorms? Compute P(r 1. 0 We have poisson trials for which the probability of success isp = 0.63 and failure is q = 0.37; k is a xed whole number 2 1. Q We have binomial trials for which the probability of success is p = 0.63 and failure is q = 0.37; k is a xed whole number 2 1. V Write out the formula for P(n) in the context of this application. (Use C(a,b) as the notation for "3 choose b".) PM = (b) Compute P(n = 12), P(n = 13), and P(n = 14). (Use 4 decimal places.) PM: pm: PM: (c) What is the probability that Susan will need from 12 to 14 contacts to get the bonus? (Use 4 decimal places.) (d) What is the probability that Susan will need more than 14 contacts to get the bonus? (Use 4 decimal places.) :1 ,0 Type here to search - K 5.4 Hmwk , Geometric & Poissor' X a: t a 6 9 O Q Q https://www.webassign.net/web/Student/AssignmentResp... A\" {3 0i 6}, n: {31:12. Write out the formula for P(n) in the context of this application. (Use C(a,b) as the notation for "3 choose b".) P(n) = (b) Compute P(n = 12), P(n = 13), and P(n = 14). (Use 4 decimal places.) ((3) What is the probability that Susan will need from 12 to 14 contacts to get the bonus? (Use 4 decimal places.) :1 (d) What is the probability that Susan will need more than 14 contacis to get the bonus? (Use 4 decimal places.) :1 (e) What are the expected value _u and standard deviation 0 of the random variable n? (Use 2 decimal places.) it: a: Interpret these values in the context of this application. O The expected contact in which the thirteenth sale occurs is pi, with a standard deviation of (7. The expected contact in which the twelfth sale occurs is u, with a standard deviation of (I. O The expected contact in which the eleventh sale occurs is p, with a standard deviation of a. O The expected contact in which the twelfth sale occurs is a, with a standard deviation of p. in! Need Help? i v ,0 Type here to search e - V 5.4 Hmwk 7 Geometric & Poissor' X t t t 6 9 O Q Q https://www.webassign.net/web/Student/AssignmentResp... A\" {3 Oi Eh 5:: g . {3 l {'5 . 5. {11 Points] DETAILS BBUNDERSTAT12 5.4.010. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Bob is a recent law school graduate who intends to take the state bar exam. According to the National Conference on Bar Examiners, about 50% of all people who take the state bar exam pass. Let n = 1, 2, 3, represent the number of times a person takes the bar exam until the rst pass. (a) Write out a formula for the probability distribution of the random variable n. (Use p and n in your answer.) P(n) = I (b) What is the probability that Bob rst passes the bar exam on the second try (n = 2)? (Use 3 decimal places.) :1 (c) What is the probability that Bob needs three attempl: to pass the bar exam? (Use 3 decimal places.) :1 (d) What is the probability that Bob needs more than three attempts to pass the bar exam? (Use 3 decimal places.) :1 (e) What is the expected number of attempls at the state bar exam Bob must make for his (rst) pass? Hint: Use p for the geometric distribution and round. E Need Help? i 6. [-I1 Points] DETAILS BBUNDERSTAT12 5.4.012. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER ,0 Type here to search VA 5.4 Hmwk - Geometric & Poissor X *Course Hero X Course Hero X Homework Help - Q&A from On X + X -> @ https://www.webassign.net/web/Student/Assignment-Resp... A Lo sd 6. [-/1 Points] DETAILS BBUNDERSTAT12 5.4.012. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Approximately 3.3% of all (untreated) Jonathan apples had bitter pit in a study conducted by the botanists Ratkowsky and Martin. (Bitter pit is a disease of apples resulting in a soggy ore, which can be caused either by overwatering the apple tree or by a calcium deficiency in the soil.) Let n be a random variable that represents the first Jonathan apple chosen at random that has bitter pit. (a) Write out a formula for the probability distribution of the random variable n. (Use p and n in your answer. ) P ( n) = (b) Find the probabilities that n = 3, n = 5, and n = 12. (Use 3 decimal places.) P ( 3 ) P (5 ) P(12) (c) Find the probability that n 2 5. (Use 3 decimal places.) (d) What is the expected number of apples that must be examined to find the first one with bitter pit? Hint: Use u for the geometric distribution and round. Need Help? Read It Watch It O W 9:34 AM Type here to search 42.F 2/11/2022- V 5.4 Hmwk , Geometric & Poissor' X t t t 6 9 O Q Q https://www.webassignnet/web/Student/AssignmentResp... A\" {3 0i Eh 5:: g . {3 l {'5 . W At Burnt Mesa Pueblo, in one of the archaeological excavation sites, the artifact density (number of prehistoric artifacts per 10 liters of sediment) was 1.1. Suppose you are going to dig up and examine 44 liters of sediment at this site. Let r = 0, 1, 2, 3, be a random variable that represent: the number of prehistoric artifacts found in your 44 liters of sediment. (a) Explain why the Poisson distribution would be a good choice for the probability distribution of r. Finding prehistoric artifacts is a rare occurrence. It is reasonable to assume the events are independent. 0 Finding prehistoric artifacts is a rare occurrence. It is reasonable to assume the events are dependent. 0 Finding prehistoric artifacts is a common occurrence. It is reasonable to assume the events are dependent. 0 Finding prehistoric artifacts is a common occurrence. It is reasonable to assume the events are independent. What is A? : Write out the formula for the probability distribution of the random variable r. (Use e, l, and r in your answer.) P(r) = (b) Compute the probabilities that in your 44 liters of sediment you will nd two prehistoric artifacts, three prehistoric artifacts, and four prehistoric artifacts. (Round your answers to four decimal places.) 2) = :l 9(3) = l:l Pm = :] ,0 Type here to search - K 5.4 Hmwk 7 Geometric & Poissor' X a: t * 6 9 O Q Q https://www.webassign.net/web/Student/AssignmentResp... A\" {3 Fl 6'\" 5:: g . {3 l {'5 . 0 Finding prehistoric artifacts is a common occurrence. It is reasonable to assume the events are independent. What is A? : Write out the formula for the probability distribution of the random variable r. (Use 6, A, and r in your answer.) P0) = (b) Compute the probabilities that in your 44 liters of sediment you will nd two prehistoric artifacts, three prehistoric artifacts, and four prehistoric artifacts. (Round your answers to four decimal places.) 2) = :l 9(2) = l:l Pm = :l (c) Find the probability that you will nd three or more prehistoric artifacts in the 44 liters of sediment. (Round your answer to four decimal places.) [:1 (d) Find the probability that you will nd fewer than three prehistoric artifacts in the 44 liters of sediment. (Round your answer to four decimal places.) :l Need Help? i i v ,0 Type here to search e - V 5.4 Hmwk , Geometric & Poissoi' X t 1: t 6 9 O Q Q https://www.webassign.net/web/Student/AssignmentResp... A\" {3 Ii 6'" H: g . {3 l {'5 . 8. [0.08/1 Points] DETAILS PREVIOUS ANSWERS BBUNDERSTAT12 5.4.017. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER A television program reported that the U.S. (annual) birth rate is about 22 per 1000 people, and the death rate is about 13 per 1000 people. (a) Explain why the Poisson probability distribution would be a good choice for the random variable r = number of births (or deaths) for a community of a given population size? 0 Frequency of births (or deaths) is a rare occurrence. It is reasonable to assume the events are dependent. O Frequency of births (or deaths) is a common occurrence. It is reasonable to assume the events are independent. 0 Frequency of births (or deaths) is a common occurrence. It is reasonable to assume the events are dependent. Frequency of births (or deaths) is a rare occurrence. It is reasonable to assume the events are independent. ' I (b) In a community of 1000 people, what is the (annual) probability of 9 births? What is the probability of 9 deaths? What is the probability of 12 births? 12 deaths? (Round your answers to four decimal places.) 9(9 births) = :] P(9 deaths) = :] P(12 births) = :] P(12 deaths) = :l (c) Repeat part (b) for a community of 1500 people. You will need to use a calculator to compute P(9 births) and P(12 births). (Round your answers to four decimal places.) P(9 births) = :] P(9 deaths) = :] P(12 births) =:] P(12 deaths) = :] ,0 Type here to search - K 5.4 Hmwk , Geometric & Poissor X s v. s 6 9 O Q Q https://www.webassign.net/web/Student/AssignmentResp... A\" {3 Fl 6'" 5:: g . {3 l {'5 . 0 Frequency of births (or deaths) is a common occurrence. It is reasonable to assume the events are dependent. Frequency of births (or deaths) is a rare occurrence. It is reasonable to assume the events are independent. V (b) In a community of 1000 people, what is the (annual) probability of 9 births? What is the probability of 9 deaths? What is the probability of 12 births? 12 deaths? (Round your answers to four decimal places.) P(Q births) = P(9 deaths) = P(12 births) = P(12 deaths) = ((2) Repeat part (b) for a community of 1500 people. You will need to use a calculator to compute P(9 births) and P(12 births). (Round your answers to four decimal places.) P(Q births) = P(9 deaths) = P(12 births) = P(12 deaths) = (d) Repeat part (b) for a community of 750 people. (Round your answers to four decimal places.) P(Q births) = P(9 deaths) = P(12 births) = P(12 deaths) = Need Help? i v ,0 Type here to search e - V 5.4 Hmwk , Geometric & Poissor' X t t t 6 9 O Q Q https://www.webassign.net/web/Student/AssignmentResp... A\" {3 0% 6'" 5:: noise.\"- Much of Trail Ridge Road in Rocky Mountain National Park is over 12,000 feet high. Although it is a beautiful drive in summer months, in winter the road is closed because of severe weather conditions. Sustained galeforce winds (over 32 miles per hour and often over 90 miles per hour) occur on the average of once every 65 hours at a Trail Ridge Road weather station. (a) Let r = frequency with which galeforce winds occur in a given time interval. Explain why the Poisson probability dis ribution would be a good choice for the random variable r. (9 Frequency of galeforce winds is a rare occurrence. It is reasonable to assume the events are independent. 0 Frequency of galeforce winds is a rare occurrence. It is reasonable to assume the events are dependent. 0 Frequency of galeforce winds is a common occurrence. It is reasonable to assume the events are independent. 0 Frequency of galeforce winds is a common occurrence. It is reasonable to assume the events are dependent. I (b) For an interval of 104 hours, what are the probabilities that r = 2, 3, and 4? What is the probability that r 10. The Poisson approximation is good because n is large, p is small, and np 1? (Use 4 decimal places.) : (d) What is the probability that r > 2? (Use 4 decimal places.) : (e) What is the probability that r > 3? (Use 4 decimal places.) : ,0 Type here to search e - K 5.4 Hmwk , Geometric & Poissor' X t t t 6 9 O Q Q https://www.webassign.net/web/Student/AssignmentResp... A\" {3 Fl 6'\" 5:: g . {3 l {'5 . Chances: Risk and Odds in Everyday Life, by James Burke, reports that only 2.7% of all local franchises are business failures. A Colorado Springs shopping complex has 142 franchises (restauranls, print shops, convenience stores, hair salons, etc.). (a) Let r be the number of these franchises that are business failures. Explain why a Poisson approximation to the binomial would be appropriate for the random variable r. The Poisson approximation is good because n is large, p is small, and np 10. O The Poisson approximation is good because n is small, p is small, and np