5. Mrs. Hoskins is going to plant her new

For a certain river, suppose the drought length Y is the number of consecutive time intervals in which the water supply remains

AnnZ [28]

Answer:

a) There is a 9% probability that a drought lasts exactly 3 intervals.

There is an 85.5% probability that a drought lasts at most 3 intervals.

b)There is a 14.5% probability that the length of a drought exceeds its mean value by at least one standard deviation

Step-by-step explanation:

The geometric distribution is the number of failures expected before you get a success in a series of Bernoulli trials.

It has the following probability density formula:

$f(x) = (1-p)^{x}p$

In which p is the probability of a success.

The mean of the geometric distribution is given by the following formula:

$\mu = \frac{1-p}{p}$

The standard deviation of the geometric distribution is given by the following formula:

$\sigma = \sqrt{\frac{1-p}{p^{2}}$

In this problem, we have that:

$p = 0.383$

So

$\mu = \frac{1-p}{p} = \frac{1-0.383}{0.383} = 1.61$

$\sigma = \sqrt{\frac{1-p}{p^{2}}} = \sqrt{\frac{1-0.383}{(0.383)^{2}}} = 2.05$

(a) What is the probability that a drought lasts exactly 3 intervals?

This is $f(3)$

$f(x) = (1-p)^{x}p$

$f(3) = (1-0.383)^{3}*(0.383)$

$f(3) = 0.09$

There is a 9% probability that a drought lasts exactly 3 intervals.

At most 3 intervals?

This is $P = f(0) + f(1) + f(2) + f(3)$

$f(x) = (1-p)^{x}p$

$f(0) = (1-0.383)^{0}*(0.383) = 0.383$

$f(1) = (1-0.383)^{1}*(0.383) = 0.236$

$f(2) = (1-0.383)^{2}*(0.383) = 0.146$

Previously in this exercise, we found that $f(3) = 0.09$

So

$P = f(0) + f(1) + f(2) + f(3) = 0.383 + 0.236 + 0.146 + 0.09 = 0.855$

There is an 85.5% probability that a drought lasts at most 3 intervals.

(b) What is the probability that the length of a drought exceeds its mean value by at least one standard deviation?

This is $P(X \geq \mu+\sigma) = P(X \geq 1.61 + 2.05) = P(X \geq 3.66) = P(X \geq 4)$ .

We are working with discrete data, so 3.66 is rounded up to 4.

Either a drought lasts at least four months, or it lasts at most thee. In a), we found that the probability that it lasts at most 3 months is 0.855. The sum of these probabilities is decimal 1. So:

$P(X \leq 3) + P(X \geq 4) = 1$

$0.855 + P(X \geq 4) = 1$

$P(X \geq 4) = 0.145$

There is a 14.5% probability that the length of a drought exceeds its mean value by at least one standard deviation

8 0

3 years ago

I need help I don’t understand :(

sveticcg [70]

Answer:

.

Step-by-step explanation:

7 0

3 years ago

Solve with a system of equations: Two angles are supplementary if the sum of their measures are 180 degrees. If one is 90 degree

julsineya [31]

Answer:

The measures of the angles are 150° and 30°.

Step-by-step explanation:

Let x and y represent the measures of the angles, with x representing the larger angle.

x + y = 180 . . . . . . the two angles are supplementary

x = 90 + 2y . . . . . one is 90° more than twice the other

___

Substituting the expression given by the second equation into the first, we have ...

(90 +2y) +y = 180

3y = 90 . . . . . . . . . . collect terms, subtract 90

y = 30 . . . . . . . . . . . divide by the coefficient of y

x = 180 -y = 150

The measures of the angles are 150° and 30°.

6 0

3 years ago

Which statements are true for the image below? Check all that apply.

Arlecino [84]

Answer:

its 1,3,4,and 7

Step-by-step explanation:

i just did it

so A,C,D,and G

3 0

3 years ago

Read 2 more answers

What is the slope of the line that passes through the pair of points (-2.5,6.1) and (-2.5,3.1)

podryga [215]

(-2.5,6.1)(-2.5,3.1).....notice how ur x values are the same. This means that u have a vertical line which has an undefined slope.

IF ur y values would have been the same, u would have had a horizontal line which has a 0 slope.

5 0

3 years ago