If 8% of the population of trees are elm trees, find the probability that in a sample in a sample of 100 trees, there are exactly 6 elm trees. assume the distribution is approximately Poisson

Question

Generate an image of a tranquil forest, composed of various types of trees, with a diverse group of a hundred representative trees marked in the foreground. In the marked group, distinguish exactly six elm trees with their distinctive features such as their serrated leaf edges and upright habit. This serene landscape scene should also subtly reflect an air of mathematical inquiry, exemplified by perhaps a pattern arrangement of trees, but without any text or numerical symbols.

If 8% of the population of trees are elm trees, find the probability that in a sample in a sample of 100 trees, there are exactly 6 elm trees. assume the distribution is approximately Poisson

Answer 1

If 8% of the population of trees are elm trees, find the probability that in a sample of 100 trees, there are exactly six elm trees. Assume the distribution is approximately Poisson.

Solution:
Since λ= n(p)= 0.08(100)=8
X=6

(2.7183)^-8 (8)^6 /6!
=0.12213168 (ANSWER)

Answer 2

i need ansower of this question

Answer 3

To find the probability that in a sample of 100 trees, there are exactly 6 elm trees, we can use the Poisson distribution. The Poisson distribution is used to model events that occur randomly over time or space, assuming a constant average rate.

In this case, we can approximate the distribution as Poisson because the number of elm trees in a sample is random and follows a certain rate (8% of the population).

To calculate the probability, we need to determine the average rate (λ) of elm trees in the sample. The Poisson distribution uses the formula:

P(x, λ) = (e^(-λ) * λ^x) / x!

Where x is the number of events we're interested in (6 elm trees in this case), e is the base of natural logarithms (approximately 2.71828), λ is the average rate (in this case, the percentage of elm trees converted to a decimal), and x! is the factorial of x.

First, convert the 8% population proportion to a decimal: 8% = 0.08.

λ = (0.08 * 100) / 100 = 0.08

Now we can substitute the values into the formula:

P(6, 0.08) = (e^(-0.08) * 0.08^6) / 6!

To find the factorial of 6 (6!), we multiply the numbers from 6 down to 1:

6! = 6 * 5 * 4 * 3 * 2 * 1 = 720

Now simplify the equation:

P(6, 0.08) = (e^(-0.08) * 0.08^6) / 720

Use a calculator to evaluate e^(-0.08) and 0.08^6:

P(6, 0.08) ≈ (0.9231 * 0.000262144) / 720

P(6, 0.08) ≈ 0.000240778 / 720

P(6, 0.08) ≈ 0.000000334

So, the probability that in a sample of 100 trees there are exactly 6 elm trees, assuming the distribution is approximately Poisson, is approximately 0.000000334.

Answer 4

If 8% of the population of trees are elm trees, find the probability that in a sample of 100 trees, there are exactly six elm trees. Assume the distribution is approximately Poisson.

Answer 5

I need an answer for this question please

Answer 6

Well, let me tell you a joke about trees first:

Why did the tree go to the dentist?

Because it had a cavity!

Now, let's get back to your question. Since we are assuming the distribution to be approximately Poisson, we can use the Poisson formula to calculate the probability. The formula is:

P(x; λ) = (e^(-λ) * λ^x) / x!

In this case, λ (lambda) represents the average number of elm trees in a sample of 100 trees. λ can be calculated as 8% of 100, which equals 8.

So, let's calculate the probability of getting exactly 6 elm trees:

P(6; 8) = (e^(-8) * 8^6) / 6!

Now, let me grab my calculator and do the math for you:

P(6; 8) ≈ 0.103

Therefore, the probability of having exactly 6 elm trees in a sample of 100 trees is approximately 0.103, or 10.3%.