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Suppose that 80 percent of trees in a forest of trees are infected with a virus,...
Many of the trees in a national forest suffer from a virus that attacks the bark...
Many of the trees in a national forest suffer from a virus that attacks the bark of the tree. Trees with this virus should be removed in order to minimize the risk to nearby trees. To estimate the proportion of trees that have this virus, a random sample of 204 trees was selected. Each selected tree was inspected and it was found that 28% of the trees in the sample had the virus. A 95% confidence interval will be used...
6. For a certain section of a pine forest, the number X of diseased trees per...
6. For a certain section of a pine forest, the number X of diseased trees per acre has a Poisson distribution with mean λ = 5. (C) Suppose we have 4 plots of forest, each one acre in size, giving 4 independent Poisson random variables, X1, X2,..., X4 with mean λ = 5. Find the probability that at least two of the plots of forest have 2 or more diseased trees per acre.
A forest originally has 10,000 trees. Suppose that the forest naturally replenishes itself by 10 percent...
A forest originally has 10,000 trees. Suppose that the forest naturally replenishes itself by 10 percent per year. That is, at the end of one year, if nothing else happened, it would have 10,000 +(0.10 × 10, 000) = 11, 000 trees. (This assumption is not biologically accurate, but it keeps the math simple). Suppose that 1,500 trees are harvested at the end of each year. - How many trees will there be at the end of two years? (Note: Base...
The Clemson Experimental Forest has 17,000 acres. In general, a healthy forest has 80 trees per...
The Clemson Experimental Forest has 17,000 acres. In general, a healthy forest has 80 trees per acre on average. a. Assume the Clemson Experimental Forest is a healthy forest. What is the expected number of trees in the Clemson Experimental Forest? b. Consider the ¼ acre immediately surrounding the point where the Lake-Lawrence trail meets the Willow Springs Trail. What is the probability that this ¼ acre has less than 40 trees?
In a forest there are trees with an average density of 5 trees per 100 yd2....
In a forest there are trees
with an average density of 5 trees per 100 yd2. Assume that the
tree trunks are perfect disks with a radius of 1 foot. (1yd = 3ft.)
We are standing 100 yd from the edge of the forest and we shoot a
bullet towards the edge. What is the probability that we will hit
one of the trees? (We will disregard the problem that trees might
‘overlap’ in that model. The bullet can be...
1. Suppose that diseased trees are distributed randomly and uniformly throughout a large forest with an...
1. Suppose that diseased trees are distributed randomly and uniformly throughout a large forest with an average of λ per acre. Let X denote the number of diseased trees in a randomly chosen one-acre plot with range, 0,1,2,.. a) What distribution can we use to model X? Write down its probability mass function (b) Suppose that we observe the number of diseased trees on n randomly chosen one-acre parcels, X1, X2, ..., X The random variables Xi, X2, ...,X, can...
1. Suppose that diseased trees are distributed randomly and uniformly throughout a large forest with an...
1. Suppose that diseased trees are distributed randomly and uniformly throughout a large forest with an average of λ per acre. Let X denote the number of diseased trees in a randomly chosen one-acre plot with range, 0,1,2,.. a) What distribution can we use to model X? Write down its probability mass function (b) Suppose that we observe the number of diseased trees on n randomly chosen one-acre parcels, X1, X2, ..., X The random variables Xi, X2, ...,X, can...
The probability of a randomly selected adult in one country being infected with a certain virus...
The probability of a randomly selected adult in one country being infected with a certain virus is 0.006. In tests for the virus, blood samples from 19 people are combined. What is the probability that the combined sample tests positive for the virus? Is it unlikely for such a combined sample to test positive? Note that the combined sample tests positive if at least one person has the virus.
The probability of a randomly selected adult in one country being infected with a certain virus...
The probability of a randomly selected adult in one country being infected with a certain virus was 0.004. In tests for the virus, blood samples from 27 people are combined. What is the probability that the combined sample tests positive for the virus? Is it unlikely for such a combined sample to test positive? Note that the combined sample tests positive if at least one person has the virus. The probability that the combined sample will test positive is?
The probability of a randomly selected adult in one country being infected with a certain virus...
The probability of a randomly selected adult in one country being infected with a certain virus was 0.004. In tests for the virus, blood samples from 27 people are combined. What is the probability that the combined sample tests positive for the virus? Is it unlikely for such a combined sample to test positive? Note that the combined sample tests positive if at least one person has the virus. The probability that the combined sample will test positive is?
In a forest there are trees
with an average density of 5 trees per 100 yd2. Assume that the
tree trunks are perfect disks with a radius of 1 foot. (1yd = 3ft.)
We are standing 100 yd from the edge of the forest and we shoot a
bullet towards the edge. What is the probability that we will hit
one of the trees? (We will disregard the problem that trees might
‘overlap’ in that model. The bullet can be...
1. Suppose that diseased trees are distributed randomly and uniformly throughout a large forest with an average of λ per acre. Let X denote the number of diseased trees in a randomly chosen one-acre plot with range, 0,1,2,.. a) What distribution can we use to model X? Write down its probability mass function (b) Suppose that we observe the number of diseased trees on n randomly chosen one-acre parcels, X1, X2, ..., X The random variables Xi, X2, ...,X, can...
1. Suppose that diseased trees are distributed randomly and uniformly throughout a large forest with an average of λ per acre. Let X denote the number of diseased trees in a randomly chosen one-acre plot with range, 0,1,2,.. a) What distribution can we use to model X? Write down its probability mass function (b) Suppose that we observe the number of diseased trees on n randomly chosen one-acre parcels, X1, X2, ..., X The random variables Xi, X2, ...,X, can...
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