Question

At Burnt Mesa Pueblo, in one of the archaeological excavation sites, the artifact density (number of...

At Burnt Mesa Pueblo, in one of the archaeological excavation sites, the artifact density (number of prehistoric artifacts per 10 liters of sediment) was 1.7. Suppose you are going to dig up and examine 47 liters of sediment at this site. Let r = 0, 1, 2, 3, ... be a random variable that represents the number of prehistoric artifacts found in your 47 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 common occurrence. It is reasonable to assume the events are dependent. Finding prehistoric artifacts is a common occurrence. It is reasonable to assume the events are independent. Finding prehistoric artifacts is a rare occurrence. It is reasonable to assume the events are independent. Finding prehistoric artifacts is a rare occurrence. It is reasonable to assume the events are dependent. What is λ? Write out the formula for the probability distribution of the random variable r. (Use e, λ, and r in your answer.) P(r) = (b) Compute the probabilities that in your 47 liters of sediment you will find two prehistoric artifacts, three prehistoric artifacts, and four prehistoric artifacts. (Round your answers to four decimal places.) P(2) = P(3) = P(4) = (c) Find the probability that you will find three or more prehistoric artifacts in the 47 liters of sediment. (Round your answer to four decimal places.) (d) Find the probability that you will find fewer than three prehistoric artifacts in the 47 liters of sediment. (Round your answer to four decimal places.)

Homework Answers

Answer #1

Finding prehistoric artifacts is a rare occurrence. It is reasonable to assume the events are independent.

λ =47*1.7/10=7.99

P(r)=e-r/r!

b)

P(2) 0.0108
P(3) 0.0288
P(4) 0.0575

c)

probability that you will find three or more prehistoric artifacts in the 47 liters of sediment =P(X>=3)=0.9861

d)

probability that you will find fewer than three prehistoric artifacts in the 47 liters of sediment =1-0.9861 =0.0139

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
At Burnt Mesa Pueblo, in one of the archaeological excavation sites, the artifact density (number of...
At Burnt Mesa Pueblo, in one of the archaeological excavation sites, the artifact density (number of prehistoric artifacts per 10 liters of sediment) was 1.9. Suppose you are going to dig up and examine 51 liters of sediment at this site. Let r = 0, 1, 2, 3, ... be a random variable that represents the number of prehistoric artifacts found in your 51 liters of sediment. (a) Explain why the Poisson distribution would be a good choice for the...
At Burnt Mesa Pueblo, in one of the archaeological excavation sites, the artifact density (number of...
At Burnt Mesa Pueblo, in one of the archaeological excavation sites, the artifact density (number of prehistoric artifacts per 10 liters of sediment) was 1.2. Suppose you are going to dig up and examine 49 liters of sediment at this site. Let r = 0, 1, 2, 3, ... be a random variable that represents the number of prehistoric artifacts found in your 49 liters of sediment. (a) Explain why the Poisson distribution would be a good choice for the...
At Burnt Mesa Pueblo, in one of the archaeological excavation sites, the artifact density (number of...
At Burnt Mesa Pueblo, in one of the archaeological excavation sites, the artifact density (number of prehistoric artifacts per 10 liters of sediment) was 1.3. Suppose you are going to dig up and examine 45 liters of sediment at this site. Let r = 0, 1, 2, 3, ... be a random variable that represents the number of prehistoric artifacts found in your 45 liters of sediment. What is λ? Write out the formula for the probability distribution of the...
At Burnt Mesa Pueblo, in one of the archaeological excavation sites, the artifact density (number of...
At Burnt Mesa Pueblo, in one of the archaeological excavation sites, the artifact density (number of prehistoric artifacts per 10 liters of sediment) was 1.8. Suppose you are going to dig up and examine 43 liters of sediment at this site. Let r = 0, 1, 2, 3, ... be a random variable that represents the number of prehistoric artifacts found in your 43 liters of sediment What is ?? Write out the formula for the probability distribution of the...
The Denver Post reported that, on average, a large shopping center had an incident of shoplifting...
The Denver Post reported that, on average, a large shopping center had an incident of shoplifting caught by security 1.4 times every three 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 an 11-hour period during which the center is open. (a) Explain why the Poisson probability distribution would be a good choice for the random variable r. -Frequency of shoplifting is a...
Flying over the western states with mountainous terrain in a small aircraft is 40% riskier than...
Flying over the western states with mountainous terrain in a small aircraft is 40% riskier than flying over similar distances in flatter portions of the nation, according to a General Accounting Office study completed in response to a congressional request. The accident rate for small aircraft in the 11 mountainous western states is 3.0 accidents per 100,000 flight operations. (a) Let r = number of accidents for a given number of operations. Explain why the Poisson distribution would be a...
USA Today reported that Parkfield, California, is dubbed the world's earthquake capital because it sits on...
USA Today reported that Parkfield, California, is dubbed the world's earthquake capital because it sits on top of the notorious San Andreas fault. Since 1857, Parkfield has had a major earthquake on the average of 1.7 times every 22 years. (a) Explain why a Poisson probability distribution would be a good choice for r = number of earthquakes in a given time interval. Frequency of earthquakes is a common occurrence. It is reasonable to assume the events are independent.Frequency of...
In his doctoral thesis, L. A. Beckel (University of Minnesota, 1982) studied the social behavior of...
In his doctoral thesis, L. A. Beckel (University of Minnesota, 1982) studied the social behavior of river otters during the mating season. An important role in the bonding process of river otters is very short periods of social grooming. After extensive observations, Dr. Beckel found that one group of river otters under study had a frequency of initiating grooming of approximately 1.7 for each 10 minutes. Suppose that you are observing river otters for 20 minutes. Let r = 0,...
A television program reported that the U.S. (annual) birth rate is about 20 per 1000 people,...
A television program reported that the U.S. (annual) birth rate is about 20 per 1000 people, and the death rate is about 8 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? Frequency of births (or deaths) is a common occurrence. It is reasonable to assume the events are dependent.Frequency of births (or deaths) is...
Tree-ring dating from archaeological excavation sites is used in conjunction with other chronologic evidence to estimate...
Tree-ring dating from archaeological excavation sites is used in conjunction with other chronologic evidence to estimate occupation dates of prehistoric Indian ruins in the southwestern United States. Suppose it is thought that a certain pueblo was occupied around 1292 A.D. (based on evidence from potsherds and stone tools). The following data give tree-ring dates (A.D.) from adjacent archaeological sites: 1189 1267 1268 1275 1275 1271 1272 1316 1317 1230 (i) Use a calculator with sample mean and standard deviation keys...