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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

2 years ago

☝︎image<br> HELP ME PLEASEE

spin [16.1K]

Answer:

7. 5

8. 33. 3333 or 100/ 3

9. 18/7

10. 30 /7

5 0

2 years ago

A trapezoid has an area of 30m^2. if all of its side lengths are tripled, what will its new area be

Norma-Jean [14]

Answer:

270

Step-by-step explanation:

Because we do not know what the side lengths are, as long as they multiply to 30m^2, it's fine

For this question, let's just say the base is 5, and the height is 6. If we triple 5, we get 15, and if we triple 6, we get 18. 15*18=270

Now what if, the sides are not 5 and 6. Will the area still be the same? Let's find out.

10*3=30 so we can say for this answer, the base is 3, and the height is 10.

10 tripled is 30, and 3 tripled is 9. 30*9=270

So as we look at these 2 answers. we can conclude that the new area, no matter the side lengths, will be 270

Hope this helpes!

5 0

3 years ago

The market sells 1 dozen bagels

PIT_PIT [208]

Answer:

market

Step-by-step explanation:

<u>Market</u>

1 dozen bagels = 12 bagels

⇒ Cost per bagel = $7.00 ÷ 12 = $0.58 (nearest cent)

<u>Bagel shop</u>

Cost per bagel = $0.60

As $0.58 < $0.60 the market is a better buy

3 0

1 year ago

Experiments on learning in animals sometimes measure how long it takes mice to find their way through a maze. The mean time is 1

Dahasolnce [82]

Answer:

<h3>Option c) $H_a:\mu$ is correct</h3><h3>The alternate hypothesis for the significance test is $H_a:\mu$ </h3>

Step-by-step explanation:

The alternate hypothesis use the sumbol for the population value

Let p be the proportion , Mean be $\mu$ and stadard deviation be $\sigma$

The null hypothesis states that population value is equal to the value mentioned in the given claim.

$H_0:\mu=18$ (by given).

The alternate hypothesis for the significance test states that the opposite of the null hypothesis(based on the claim )

∴ $H_a:\mu$

The symbol "<" because we want to test if the maze is completed faster and thus if the time has decreased.

<h3>∴ option c) $H_a:\mu$ is correct.</h3>

3 0

2 years ago