I have no idea on how to does this... and neither did half of my class. Help?!?!

Grasshoppers are distributed at random in a large field according to a Poisson process with parameter a 5 2 per square yard. How

HACTEHA [7]

In this question, the Poisson distribution is used.

Poisson distribution:

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:

$P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}$

In which

x is the number of sucesses

e = 2.71828 is the Euler number

$\mu$ is the mean in the given interval.

Parameter of 5.2 per square yard:

This means that $\mu = 5.2r$ , in which r is the radius.

How large should the radius R of a circular sampling region be taken so that the probability of finding at least one in the region equals 0.99?

We want:

$P(X \geq 1) = 1 - P(X = 0) = 0.99$

Thus:

$P(X = 0) = 1 - 0.99 = 0.01$

We have that:

$P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}$

$P(X = 0) = \frac{e^{-5.2r}*(5.2r)^{0}}{(0)!} = e^{-5.2r}$

Then

$e^{-5.2r} = 0.01$

$\ln{e^{-5.2r}} = \ln{0.01}$

$-5.2r = \ln{0.01}$

$r = -\frac{\ln{0.01}}{5.2}$

$r = 0.89$

Thus, the radius should be of at least 0.89.

Another example of a Poisson distribution is found at brainly.com/question/24098004

3 0

3 years ago

Can someone please help me with this problem?

Sophie [7]

Answer:

20

Step-by-step explanation:

4 x 5 = 20

8 0

3 years ago

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A rectangular magazine cover is photocopied by using a scale factor of One-third. The length of the photocopy of the magazine co

seraphim [82]

Answer: "reduced by a factor of One-third."

Step-by-step explanation:

Suppose that the original magazine has a length L and a width W.

If it is photocopied using a scale factor of K, then the measures of the photocopy will be:

length = K*L

Width = K*W

In this case, the scale factor is K = 1/3, then the measures of the photocopy will be:

length = (1/3)*L = L/3

Width = (1/3)*W = W/3

For usual notation:

When k > 1, we have an enlargement by a factor k

when 0 < k < 1, we have a reduction by a factor k

in this case, k = 1/3, then:

We have a reduction by a factor of 1/3

The correct option is:

"reduced by a factor of One-third."

7 0

3 years ago

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A survey was conducted from a random sample of 8225 Americans, and one variable that was recorded for each participant was their

solniwko [45]

Answer:

d. skewed right

Step-by-step explanation:

The shape of the given distribution is rightly skewed. For a symmetric distribution mean and median are equal and if mean is greater than median then the distribution is rightly skewed and if mean is less than median then the distribution is skewed left.

In the given distribution mean is greater than median and so the given distribution is skewed right.

8 0

3 years ago

Simplify the expression. Write your answer as a power.

Gnesinka [82]

Answer:

(3/7)^7

Step-by-step explanation:

When multiplying exponents we can use the formula: a^m x a^n = a^m+n.

In this case, we can plug in 3/7 for a, and their respective exponents as m and n.

(3/7)^3 x (3/7)^4= (3/7)^3+4= (3/7)^7

Hope this helps!

:)

8 0

2 years ago

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