Coral bought some stock at $25 a share the stock increased to 1 1/2 Times its value how much is that stock per-share

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

This summer, the Harris family wants to go to San Diego, California. They estimate that their destination is about 658 miles fro

Over [174]

A little more than 8 days. If you divide 658 by 75 you should get the exact answer

4 0

3 years ago

What is the solution to the equation? 9.1k = 63.7

Natalija [7]

Answer:

k = 7

Step-by-step explanation:

9.1k = 63.7

/9.1 /9.1

k = 7

Check your answer:

9.1k = 63.7

9.1 (7) = 63.7

63.7 = 63.7

This statement is true.

Hope this helps!

4 0

2 years ago

Read 2 more answers

Estimate 53.83-36.464 by first rounding each number to the nearest whole number.

Free_Kalibri [48]

Answer:

18

Step-by-step explanation:

53.83 rounds to 54

36.464 rounds to 36

54-46=18

7 0

3 years ago

Read 2 more answers

Drag numbers to use a negative factor to factor the expression -59 + 15h - 25. Numbers may be used once, more than once, or not

koban [17]

Answer:

$-5(g - 3h + 5)$

Step-by-step explanation:

Given

$-5g + 15h - 25$

Required

Factor using a negative factor

Express each term as a factor of -5

$-5*g - 5*-3h - 5 * 5$

Factor out -5

$-5(g - 3h + 5)$

Hence:

The factored form of $-5g + 15h - 25$ is $-5(g - 3h + 5)$

7 0

3 years ago